∶ ( )
1. The amplitude of a complex number isisis
a) 0 b) / c) d)
2.The amplitude of the quotient of two complex numbers is
a) the sum of their amplitudes b) the difference of their amplitudes
c) the product of their amplitudes d) the quotient of their amplitudes
3. The = + then = a) + b) + c) − d) imaginary
| | 4. If & are any two complex numbers, then | . | isisis
| | | | | | | | | | a)a)a) | | b) | . | c) | || | d) | | | |
555.5... → + =
a) b) − c) d)
666.The6.The equation | + | + | − | = represents
a) Circle b) ellipse c) parparabolaabola d) hyperbola
777.The7.The equation | + | = | − | represents
a) Circle b) ellipse c) parparabolaabola d) Real axis
888.The8.The equation | + | = √ | − | represents
a) Circle b) ellipse c) parparabolaabola d) hyperbola
999.The9.The equation | + | + | − | = represents
a) Circle b) a st. line c) parabola d) hyperbohyperbolalalala
101010.The10.The equation | − | = | − | represents
a) Circle b) a st. line c) parabola d) hyperbola 111111.The11.The equation | − | + | − | = represents
a) Circle b) a st. line c) parabola d) hyperbola 121212.The12.The equation = represents
a) Circle b) a st. line c) parabola d) hyperbola 131313.The13.The equation = / represents 1
a) CiCirclercle b) a st. line c) paparabolarabola d) hyperbola ( ) ( ) , ≠ , ≠ 141414.14. Let ( ) = | | and ( ) = , = , =
a) both f(z) & g(z) are continues at the origin
b) both f(z) & g(z) are not continues at the origin
c) f(z) continues at the origin & g(z) is notnot ccontinuesontinues at the origin
d) f(z) is not continues at the origin & g(z)g(z) is continues at tthehe origin
151515.The15.The multiplicative identity if C is
a)(0,0) b) (1,1) c) (0,1) d) (1,0)
161616. =
a) 1+i b) 11----ii c) 1 d) ---1-111 171717.17. If is a complex number such that + + = then = a) b) c) 0 d) 1 181818.18. If p is a complex number & | | = thththenthen is
a) i b) ---i-i c) 1 d) ---1-111 191919.19. .. . . → =
a) b) c) d) 8d) 8
202020.20. If & are the image of the complex plane of two diametricdiametricallyally opposite point on the Rieman’s
sphere then is
a) 0 b) 1 c) ---1-1 d)
∶
111 666 111111 161616 212121 222 777 121212 171717 222222 333 888 131313 181818 232323 444 999 141414 191919 242424 555 101010 151515 202020 252525
2
∶ ( ) 111.1. The function = is analytic
a) for all z b) for all z excexceptept 1,1,----11 c) for all z except , − d) for all z except +
222.2. Which of the following is not an entire function ? a) b) c) − d)d)d) d)
333.3. Which of the following is called CC----RR equation for the function ( ) = + to be analytic at z ?
a) = − & = b) = & = − c) = & = d) = − & =
444.4. Which of the following is called CC----RR equation for polar coordinates ??? a) = & = − b) = & =
c)c)c) = & = − d) = & =
555.Define5.Define ( ) = zzz≠0z≠0 then
a) → ( ) does not exists b) f(z) is continues at z=0
b) f(z) does not continues at z=0 d)d) → ( ) =
666.6...ForFor the function ( ) = + to be differentiable
a) necessary & sufficient b) necessary & not sufficient
b) not necessary & sufficient d) none
12.For the function ( ) = + to be differentiable ,which of the following is truetrue
a) , , , exists b) = & = − holholholdsholdsdsds
b) , , , exexexistsexists & continuous d) all
, ≠ 777.7. Let ( ) = then f(z) at z=0 , =
a) f(z) continues b) f(z) not continuecontinuess c) f(z) is well d) none
888.For8.For the function f(z) .a poinpointt is said to be singular point if
a) f(z) is analytic at b) f(z) is not analytic at c) f(z) is continues at n) none ( ) 999.For9.For the function ( ) = ( )( ) which of the following is true
a) z = ---2-2 is a zero of order 3 b) a) z = 1 is a pole ooff order 2 c) a) z = 2 is a pole of order d) allall
101010.For10.For the function ( ) = is 3
a) entire function b) differentiable at z ===2=2 c) a) z = 2 is a pole of order d) all 11.11.11. If ( ) = − + + is differentiable at every point ,the constants
a) 2b=a b) 4b=a cc)) 2a=b d) a=b 121212.The12.The function ( ) = | | isisis
a) differentiable at z = 0 b) no whewherree differentiable c) not harmonic d) differedifferenntiabletiable at z ≠ 0
131313.If13.If ( ) = + is analytic & = ( − ) then ( ) = a) + b) − c) + / d) − /
141414.If14.If ( ) = + is analytic & = then ( ) = a) + b) + c) + d) − / 151515.15. If ( ) = + − + − + is analytic ,then the vvaluealue of a, b are respectuallyrespectually
a) ---1,1-1,1 b) ---1,2-1,2 c) 1,1,----11 c) 2,2,----1111 161616.16. If ( ) = − + + is differentiable at every point ,the constants
a) 2b=a b) 4b=a cc)) 2a=b d) a=b 171717.17. If = + − is harmonic , then the value of m is
a) 3 b) 2 c) 0 d) 1 181818.18. If the function ( ) = , + =
a) − b) ( ) + ( ) c) ( ) + ( ) d) + +
191919.Any19.Any two harmonic conjugates of a given harmonic function u(x,y) differ by
a) x b) y c) xy d) constant
202020.20. The image of the strip 0 a) < < 1 b) < < 1 c) < < 2 d) < < 2 ∶ 111 666 111111 161616 212121 222 777 121212 171717 222222 333 888 131313 181818 232323 444 999 141414 191919 242424 555 101010 151515 202020 252525 4 ∶ ( ) 111.1. The radius of convergence of ∑ ! isisis a) ∞ b) c) / d) 222.2. The radius of convergence of ∑ isisis a) ∞ b) c) / d) 333.3. The radius of convergence of ∑ ( )( ) isisis a) ∞ b) c) / d) ! 444.4. The radius of convergence of ∑ ! isisis a) ∞ b) c) / d) ( ) 555.5. The radius of convergence of ∑ ( − ) isisis a) ∞ b) c) / d) 666.6. The radius of convergence of ∑( + ) isisis a) ∞ b) c) / d) 777.7. The radius of convergence of ∑ + isisis a) ∞ b) c) / d) 888.The8.The invariants points of = isisis a) 3,3,----55 b) 3,3,----33 c) 3,5 d) ---3,-3,3,3,----5555 999.The9.The invariants points of = isisis a) , − b) , c) ± d) ± 101010.The10.The invariants pointpointss of = isisis a) , − b) , c) ± d) ± 111111.The11.The invariants points of = isisis a) , − b) , c) ± d) ± 11121222.The.The invariants points of = isisis 5 a) , − b) , c) ± d) ± 131313.The13.The invariants points of = isisis a) , − b) , c) ± d) ± 141414.The14.The invariants points of = isisis a) ± √ b) ± √ c) ± d) ± 151515.The15.The transformation = + is said to be a) Translation b) Magnification c) Rotation d) Inversion 161616.The16.The transformation = is said to be a) Translation b) Magnification &&& Rotation ccc)c) Inversion d) none 171717.The17.The transformation = / is said to be a) Translation b) Magnification c) Rotation d) Inversion & Reflection 181818.The18.The curve & their images under = / are given below , state which of the following is truetrue 1) Circle not thro’ 0 into circle not thro’ 0 2) St. line not thro’ 0 into circle thro’ 0 3) Circle thro’ 0 into St.line not thro’ 0 4) St.line thro’ 0 into St.line thro’ 0 a) 1,2,3 b) 2,3,4 c) 1,2,3,4 d) 3,4 191919.The19.The angle of rotatirotationon at z = 1+i under the map = isisis a) 45 b) 0 c)c) 90 d) 180 20.The image of the circle | − | =underunder the map = / isisis a) circle b) st.line c) square d) rectangle ∶ 111 666 111111 161616 212121 222 777 121212 171717 222222 333 888 131313 181818 232323 444 999 141414 191919 242424 555 101010 151515 202020 252525 6 ∶ ( & ) 111.1. The image of the strip 0 a) < < 1 b) < < 1 c) < < 2 d) < < 2 222.2. The image of the strip 0 < x <1 under the transftransformationormation = isisis a)a)a) > 1 b) = c) < < 1 d) ) − < < 0 3. The image of the strip 0 < x <1 under the transformation + = isisis a) + = / b) = / c) = / d) none 444.4. The image of the strip 0 < y <1 under the transftransformationormation = / isisis a) + + > 0 b) − − > 0 c) + > 0 d) none 555.5. The image of the strip 0 < y <1<1/2c/2c under the transformation = / isisis a) + + > 0 b) − − > 0 c) + > 0 d) none 666.6. The transformation = / transforms a) circle not through the origin in the zz---- plane into the circle through the origin in the ww----planeplane b) circle through the origin in the zz---- plane into the st.line passing through the origin in the ww----planeplane c) st.line not through the origin in the zz---- plane into the circle through the origin in the ww----planeplane d) st.line through the origin in ththee ze z-z--- plane into the st.line passing through the origin in the ww----planeplane 777.The7.The transformation = transforms the imaginary axis in the Z axis into a) a unit circle with center at origin in the W plaplanene b) a circle of radius 2 with center at origin in the W plane c) a straight line in the W plane d) an ellipse in the W plane 888.The8.The bilinear transformation that map the points = , = − , = ∞ = − , = − − , = isisis a)a)a) a) = b) = c) = d) = 999.The9.The bilinear transformation that map the points = ∞, = , = = , = , = ∞ isisis a)a)a) a) = / b) = − / c) = d) = 101010.The10.The bilinear transformation that map the points = , = − , = − = , = , = isisis 7 a)a)a) a) = ( ) b) = (− ) c) = ( ) d) = (− ) ( ) 111111.11... If ( ) is an entire function & if = then a) z=a lies inside C b) z=a lies on tthehe boundary of C c) z=a lies outsideoutside of C d) none ( ) 121212.12. If ( ) is analytic with in & on C & z=a lies inside C, then a) 0 b) ( ) c) ( ) d) 131313.If13.If f(z) is analytic in a simple closed curve C ,t,thenhen ( ) isisis a) 0 b) ( ) c) ( ) d) 141414.If14.If C is the positively oriented circl | | = ,then isisis a) 0 b) c) ( ) d) − 15. If C is the unit circle | | = , then ( ) is a) 0 b) c) + d) − 161616.16. If C is the unit circle | | = , then is a) 0 b) c) d) 171717.17. If C is a strigh line from z=0 to z=4+2i , then is a) 0 b) + c) − d) + 181818.18. If C is the unit circle | | = , then is a) 0 b) c) d) 191919.19. If C is the unit circle | | = , then is a) 0 b) c) d) 202020.20. If C is the unit circle | | = , then is a) 0 b) c) d) ∶ 111 666 111111 161616 212121 222 777 121212 171717 222222 333 888 131313 181818 232323 444 999 141414 191919 242424 555 101010 151515 202020 252525 8 ∶ ( ) 1.1.1. If C is the unit circle | | = , then is a) 0 b) c) d) 222.2. If C is the unit circle | | = , then is a) 0 b) c) d) 333.3. If C is the unit circle | | = , then is a) 0 b) c) d) 444.4. If C is the unit circle | | = , then is a) 0 b) c) d) 5. If C is the unit circle | | = , then is a) 0 b) c) d) 6. If C is the circle | − | = , then is a) 0 b) c) d) 777.7. If C is the circle | − | = , then is a) 0 b) c) d) 888.8. If C is the circle | | = , then ( ) is a) 0 b) c) d) − 999.9. If C is ththee circle | | = , then isisis a) 0 b) c) d) 101010.10. If C is the circle | | = , then ( ) is a) 0 b) – / c) d) − 111111.11. If C is the circle | | = , then is a) 0 b) c) d) − 9 121212.12. If C is the circle | + | = , then is a) 0 b) c) d) − 131313.13. If C is the circle | | = , then is a) 0 b) c) d) − 26. If C is the circle | | = , then is a) 0 b) c) d) 141414.14. If C is | | = < 1 then isisis a) 0 b) c) d) 151515.15. If C is the circle | | = , then is a) / b) / c) d) 161616.16. If C is the circle | | = , then ( ) is a) / b) / c) d) − 171717.17. If C is the circle | | = , then is a) / b) / c) d) − 181818.18. If C is the circle | | = , then ( ) is a) / b) / c) d) − 191919.If19.If C is a closeclosedd curve enclosing the origin , then the value of isisis a) 0 b) − c) d) 202020.20. If C is | | = then isisis a) 0 b) c) d) ( )! ∶ 111 666 111111 161616 212121 222 777 121212 171717 222222 333 888 131313 181818 232323 444 999 141414 191919 242424 10 555 101010 151515 202020 252525 ∶ ( ) 111.1. If C is the positively oriented circle | − | = , then is a) b) − c)c)c) d) 222.The2.The poles of z cot z are a) b) c) ( + ) d) ( − ) 3.3.3.The3.The residue of ( ) = ( ) at z=2 is a) 1/5 b) 1/4 c) 1/3 d) 3/3/22 444.The4.The residue of ( ) = ( ) at a simple pole is a) 1/5 b) 1/4 c) 1/3 d) 1/2 5.The residue of ( ) = at z=0 is a) 1/5 b) 1/4 c)c) 1/3 d) ---1/2-1/2 666.The6.The residue of ( ) = at = / is a) 1/5 b) 1/4 c) 1/3 d) − 777.The7.The residue of ( ) = areareare a) 1/2 b) − / c) / d) − / 888.The8.The residue of ( ) = at z=0 is a) 1/5 b) 1/4 c)c) 1/3 d) 3 999.The9.The residue of ( ) = ( ) at z=0 is a) 1/5 b) 1/4 c)c) 1/3 d) ---3/4-3/4 101010.The10.The residue of ( ) = – at = is a) 1/5 b) 1/4 c) 5c) 5/35/3 d) − 111111.The11.The residue of ( ) = ( ) at = is a) cos 1 b) sin 1 c) 1/3 d) − / 121212.The12.The residue of ( ) = at = is 11 a) 1/5 b) 1/4 c)c) 1/3 d) / 131313.13. If C is the circle | | = / , then ( )( ) is a) 0 b) c) d) − 141414.14. If C is the circle | | = , then ( ) is a) 0 b) – / c) / d) − 151515.15. If C is the circle | − | = , then is a) 0 b) – c) d) − 16. If C is the circle | − | = , then is a) 0 b) – c) ( − ) d) − 171717.The17.The singular point of ( ) = ( ) areareare a) 0,i , ---i-i b) , , − c) , d) , − 181818.18... For ( ) = ( ) ; Z=1 is a a) Removable singularity b) Pole of order 2 c)simple pole d) Essential singulsingularityarityarityarity 191919.19. For ( ) = ( − ) ( ) ; Z= ---3-333 is ais a a) Removable singularity b) Pole of order 1 c)simple pole d) Essential singularity 202020.20. For ( ) = ( ; Z= 0 is a a) Removable singularity b) Pole of order 3 c)simple pole d) Essential singularity 21.21.21. The function ( ) = , = isisis a) not a singular point b) a removableremovable singularity c) simple pole d) essentialessential ssingularityingularity 222222.The22.The Taylor’s expansion of n about the origin is a) + ! + ! + ⋯ b) − ! + ! − ⋯ c) + + ! + ! + ⋯ d) − ! + ! − ⋯ 12 23. Maclaurin’s expansion − ! + ! − ⋯ isisis a)a)a) a) b)b)b) b) c) ( + ) d) 242424.In24.In | | ≤ ,the series ∑ isisis a) convergent but not uniform b) divergent c) uniformly convergent d) neither convergent nor divergent 252525.25. in the open disc | | < 1 , then the series + + + + ⋯ isisis a) uniformly convergent b) convergentconvergent c) divergent d) absolutely converconvergentgent 262626.The26.The Taylor’s expansion of n about the origin is a) + ! + ! + ⋯ b) − ! + ! − ⋯ c) + + ! + ! + ⋯ d) − ! + ! − ⋯ 272727.27. The Taylor’s expansion of n ( + ) about the origin is a) + + + ⋯ b) − + − ⋯ c) – − − − ⋯ d) − ! + ! − ⋯ 282828.Tailar’s28.Tailar’s series for 11/z/z about z = 1 is a) + + + + ⋯ b) + ( − ) + ( − ) + ⋯ c) − ( − ) + ( − ) − ⋯ d) + ! + ! + ⋯ 292929.The29.The expansion ( )( ) = − + + + ⋯ − + + + ⋯ isisis a) not a valued function b) valued in < | | < 2 c) valued in | | < 1 d) valued in | | > 2 303030.The30.The only singularity of a single value function f(f(z)z) are poles of order 1,2 & at z = ---1-1 & z = 2 with rereresidueresidue at these poles 1 & 2 resp. ( ) = & ( ) = the function f(z) is a) + + + ( ) b) + + c) + ( ) d) + + ( ) ∶ 111 666 111111 161616 212121 262626 222 777 121212 171717 222222 272727 333 888 131313 181818 232323 282828 444 999 141414 191919 242424 292929 555 101010 151515 202020 252525 303030 13 ∶ ( − ) 1. The amplitude of a complex number isisis a) 0 b) / c) d) 2.The amplitude of the quotient of two complex numbers is a) the sum of their amplitudes b) the difference of their amplitudes c) the product of their amplitudes d) the quotient of their amplitudes 3. The = + then = a) + b) + c) − d) imaginary | | 4. If & are any two complex numbers, then | . | is | | | | | | | | | | a) | | b) | . | c) | || | d) | | | | 5. The function = is analytic a) for all z b) for all z except 1,1,----11 c) for all z except , − d) for all z except + 6. Which of the following is not an entire function ? a) b) c) − d)d)d) d) 7. If C is | | = < 1 then isisis a) 0 b) c) d) ( ) 8. If ( ) is an entire function & if = then a) z=a lies inside C b) z=a lies onon tthehe boundary of C c) z=a lies outsideoutside of C d) none ( ) 9. If ( ) is analytic with in & on C & z=a lies inside C, ththenen a) 0 b) ( ) c) ( ) d) 10. Which of the following is called CC----RR equation for the function ( ) = + to be analytic at z ? a) = − & = b) = & = − c) = & = d) = − & = 11.The Taylor’s expansion of n about the origin is 14 a) + ! + ! + ⋯ b) − ! + ! − ⋯ c) + + ! + ! + ⋯ d) − ! + ! − ⋯ 12. The Taylor’s expansion of n ( + ) about the origin is a) + + + ⋯ b) − + − ⋯ c) – − − − ⋯ d) − ! + ! − ⋯ 13. If & are the image of the complex plane of two diametricdiametricallyally opposite point on the Rieman’s sphere then is a) 0 b) 1 c) ---1-1 d) 14. in the open disc | | < 1 , then the seseriesries + + + + ⋯ isisis a) uniformly convergent b) convergentconvergent c) divergent d) absolutely converconvergentgent 15. If C is the unit circle | | = , then is a) 0 b) c) d) 16. If C is the circle | | = , then is a) 0 b) c) d) 17.17.17. 17. → + = a) b) − c) d) 18. The radius of convergence of ∑ ! isisis a) ∞ b) c) / d) 19. The image of the strip 0 a) < < 1 b) < < 1 c) < < 2 d) < < 2 20. If C is the circle | | = , then is a) / b) / c) d) 21. If C is the circle | + | = , then is a) 0 b) c) d) − 22.The equation | + | + | − | = represrepresentsentsentsents a) Circle b) ellipse c) parparabolaabola d) hyperbola 23. Maclaurin’s expansion − ! + ! − ⋯ isisis 15 a)a)a) a) b)b)b) b) c) ( + ) d) 24.The invariantinvariantss points of = isisis a) 3,3,----55 b) 3,3,----33 c) 3,5 d) ---3,-3,3,3,----5555 25.The bilinear transformation that map the points = ∞, = , = = , = , = ∞ isisis a)a)a) a) = / b) = − / c) = d) = 26. If C is the circle | | = , then is a) 0 b) c) d) 27.The Taylor’s exexpansionpansion of n about the origin is a) + ! + ! + ⋯ b) − ! + ! − ⋯ c) + + ! + ! + ⋯ d) − ! + ! − ⋯ 28.In | | ≤ ,the series ∑ isisis a) convergent but not uniform b) divergent c) uniformly convergent d) neither convergent nor divergent ( ) ( ) , ≠ , ≠ 29. Let ( ) = | | and ( ) = , = , = a) both f(z) & g(z) are continues at the origioriginn b) both f(z) & g(z) are not continues at the origin c) f(z) continues at the origin & g(z) is notnot ccontinuesontinues at the origin d) f(z) is not continues at the origin & g(z)g(z) is continues at the origin 30.If ( ) = + is analytic & = ( − ) then ( ) = a) + b) − c) + / d) − / 31.The multiplicative identity if C is a)(0,0) b) (1,1) c) (0,1) d) (1,0) 323232. = a) 1+i b) 11----ii c) 1 d) ---1-111 33. If is a complex number such that + + = then = a) b) c) 0 d) 1 16 34. If p is a complex number & | | = then is a) i b) ---i-iii c) 1 d) ---1-111 35.If C is a closed curve enclosing the origin , then the value of isisis a) 0 b) − c) d) 36.If ( ) = + is analytic & = then ( ) = a) + b) + c) + d) − / 37. If ( ) = + − + − + is analytic ,then the value of a, b are respectualrespectuallyly a) ---1,1-1,1 b) ---1,2-1,2 c) 1,1,----11 c) 2,2,----1111 38.The residue of ( ) = ( ) at a simple pole is a) 1/5 b) 1/4 c) 1/3 d) 1/2 39. If C is the circle | | = , then is a) 0 b) c) d) − 40.The transformation = transforms the imaginary axis in the Z axis into a) a unit circle with center at origin in the W plaplanene b) a circirclecle of radius 2 with center at origin in the W plaplanene c) a straight line in the W plane d) an ellipse in the W plane 41.The bilinear transformation that map the points = , = − , = ∞ = − , = − − , = isisis a)a)a) a) = b) = c) = d) = 42.The invariants points of = isisis a) ± √ b) ± √ c) ± d) ± 43.The poles of z cot z are a) b) c) ( + ) d) ( − ) 44. If = + − is harmonic , then the value of m is a) 3 b) 2 c) 0 d) 1 45.The residue of ( ) = ( ) at z=2 is 17 a) 1/5 b) 1/4 c)c) 1/3 d) 3/2 46. .46. . . → = a) b) c) d) 8d) 8 46. If ( ) = − + + is differentiable at every point ,the constants a) 2b=a b) 4b=a cc)) 2a=b d) a=b 47.The angle of rotation at z = 1+i under the map = isisis a) 45 b) 0 c)c) 90 d) 180 48.Tailar’s series for 1/z about z = 1 is a) + + + + ⋯ b) + ( − ) + ( − ) + ⋯ c) − ( − ) + ( − ) − ⋯ d) + ! + ! + ⋯ 49.The function ( ) = | | isisis a) differentiable at z = 0 b) no wherwheree differentiable c) not harmonic d) ddifferenifferentiabletiable at z ≠ 0 50. If the function ( ) = , + = a) − b) ( ) + ( ) c) ( ) + ( ) d) + + 51.The image of the circle | − | =underunder the map = / isisis a) circle b) st.line c) square d) rectangle 52. If C is | | = then isisis a) 0 b) c) d) ( )! 53.The singular point of ( ) = ( ) areareare a) 0,i , ---i-i b) , , − c) , d) , − 54.Any two harmonic conjugates of a given harmonic function u(x,y) differ by a) x b) y c) xy d) constant 55. The function ( ) = , = isisis a) not a singular point b) a removableremovable singularity c) simple pole d) essentialessential ssingularityingularity 53.The residue of ( ) = areareare 18 a) 1/2 b) − / c) / d) − / 54. The radius of convergence of ∑ + isisis a) ∞ b) c) / d) 55.The bilinear transformation that map the points = , = − , = − = , = , = isisis a)a)a) a) = ( ) b) = (− ) c) = ( ) d) = (− ) 56. If C is the positively oriented circle | − | = , then is a) b) − c)c)c) d) 57. The transformation = / transforms a) circle not through the origin in the zz---- plane into the circle through the origin in the ww----planeplane b) circcirclele through the origin in the zz---- plane into the st.line passing through the origin in the ww----planeplane c) st.line not through the origin in the zz---- plane into the circle through the origin in the ww----planeplane d) st.line through the origin in the zz---- plane into the st.line passing through the origin in the w-w---planeplane 58.The only singularity of a single value function f(z) are poles of order 1,2 & at z = ---1-1 & z = 2 with residue at these poles 1 & 2 rresp.esp. ( ) = & ( ) = the function f(z) is a) + + + ( ) b) + + c) + ( ) d) + + ( ) 59.The expansion ( )( ) = − + + + ⋯ − + + + ⋯ isisis a) not a valued function b) valued in < | | < 2 c) valued in | | < 1 d) valued in | | > 2 ∶ 111 111111 212121 313131 414141 515151 222 121212 222222 323232 424242 525252 333 131313 232323 333333 434343 535353 444 141414 242424 343434 444444 545454 555 151515 252525 353535 454545 555555 666 161616 262626 363636 464646 565656 777 171717 272727 373737 474747 575757 888 181818 282828 383838 484848 585858 19 999 191919 292929 393939 494949 595959 101010 202020 303030 404040 505050 606060 20