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Compex Analysis ( ! ) 1. The amplitu.e of a comple2 number isisis a) 0 b) 89: c) 8 .) :8 2.The amplitu.e of the quotient of two comple2 numbers is a) the sum of their amplitu.es b) the .ifference of their amplitu.es c) the pro.uct of their amplitu.es .) the quotient of their amplitu.es 3. The ? = A B then ?C = : : : : : : a) AB b) A B c) DB .) imaginary J ? K ?: J 4. If ? I ?: are any two comple2 numbers, then J ?.?: J isisis J ? K ?: J J ? K ?: J J ? K ?: J J J J J a)a)a) J ?: J b) J ?. J c) J ?: JJ? J .) J ? J J ?: J : : 555.5...MNO?P:Q: A B R = a) S b) DS c) T .) U 666.The6.The equation J? A UJ A J? D UJ = W represents a) Circle b) ellipse c) parparabolaabola .) hyperbola 777.The7.The equation J? A ZJ = J? D ZJ represents a) Circle b) ellipse c) parparabolaabola .) Real a2is 888.The8.The equation J? A J = ]:J? D J represents a) Circle b) ellipse c) parparabolaabola .) hyperbola 999.The9.The equation J?A:J A J?D:J = U represents a) Circle b) a st. line c) parabola .) hyperbohyperbolalalala 101010.The10.The equation J:? D J = J?D:J represents a) Circle b) a st. line c) parabola .) hyperbola : : 111111.The11.The equation J? D J A J?D:J = U represents a) Circle b) a st. line c) parabola .) hyperbola ?a 121212.The12.The equation !_ `?a b = c represents a) Circle b) a st. line c) parabola .) hyperbola ?a 131313.The13.The equation !_ `?Kb = 89d represents 1 a) CiCirclercle b) a st. line c) paparabolarabola .) hyperbola d d h ? (K)aB (a) , ? i W : : , ? i W 141414.14. eet f(?) = g J?J j an. _(?) = k KB j W , ? = W W , ? = W a) both f(l) I g(l) are continues at the origin b) both f(l) I g(l) are not continues at the origin c) f(l) continues at the origin I g(l) is notnot ccontinuesontinues at the origin .) f(l) is not continues at the origin I g(l)g(l) is continues at tthehe origin 151515.The15.The multiplicatime i.entity if C is a)(0,0) b) (1,1) c) (0,1) .) (1,0) 8 8 S KSKS 161616. n 8 8o = KSaS a) 1Ai b) 11ppppii c) 1 .) ppp1p111 : d 171717.17. If q is a comple2 number such that q A q A = W then q = : a) q b) q c) 0 .) 1 ar 181818.18. If p is a comple2 number I JrJ = thththenthen stras is a) i b) pppipi c) 1 .) ppp1p111 : ? aU 191919.19. .. .MNO. ?P: ` ?a: b = a) : b) U c) .) 8.) 8 202020.20. If ? I ?: are the image of the comple2 plane of two .iametric.iametricallyally opposite point on the Riemanus sphere then ?CCCC?CC:C is a) 0 b) 1 c) ppp1p1 .) vw! cB 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 : ( vB f ) : ? K 111.1. The function w = ?:a is analytic a) for all l b) for all l e2ce2ceptept 1,1,pppp11 c) for all l e2cept , D .) for all l e2cept A : 222.2. xhich of the following is not an entire function y ? a? : a) b) c) ? D .).).)Mz{.) ? 333.3. xhich of the following is calle. CCppppRR equation for the function f(?) = A to be analytic at l y a) = DB I B = b) = B I B = D c) = B I B = .) = D I B = B 444.4. xhich of the following is calle. CCppppRR equation for polar coor.inates yyy a) ! = | I | = D! b) ! = ! | I ! | = ! c)c)c) ! = ! | I ! | = D! .) ! ! = | I ! | = ! ? 555.Define5.Define f(?) = ? llli0li0 then a) MNO?PW f(?) .oes not e2ists b) f(l) is continues at l=0 b) f(l) .oes not continues at l=0 .).) MNO?PW f(?) = 666.6...ForFor the function f(?) = A to be .ifferentiable a) necessary I sufficient b) necessary I not sufficient b) not necessary I sufficient .) none 12.For the function f(?) = A to be .ifferentiable ,which of the following is truetrue a) , B , B, e2ists b) = B I B = D holholhol.shol.s.s.s b) , B , B, e2e2e2istse2ists I continuous .) all ? , ? i W 777.7. eet f(?) = g ? j then f(l) at l=0 , ? = W a) f(l) continues b) f(l) not continuecontinuess c) f(l) is well .) none 888.For8.For the function f(l) .a poinpointt ?W is sai. to be singular point if a) f(l) is analytic at ?W b) f(l) is not analytic at ?W c) f(l) is continues at ?W n) none d (?K:) 999.For9.For the function f(?) = (?a:)(?a): which of the following is true a) l = ppp2p2 is a lero of or.er 3 b) a) l = 1 is a pole ooff or.er 2 c) a) l = 2 is a pole of or.er .) allall 101010.For10.For the function f(?) = ?C is 3 a) entire function b) .ifferentiable at l ===2=2 c) a) l = 2 is a pole of or.er .) all : : 11.11.11. If f(?) = Q DB RA BA is .ifferentiable at emery point ,the constants a) 2b=a b) 4b=a cc)) 2a=b .) a=b : 121212.The12.The function f(?) = J?J isisis a) .ifferentiable at l = 0 b) no whewherree .ifferentiable c) not harmonic .) .iffere.ifferenntiabletiable at l i 0 131313.If13.If f(?) = A is analytic I = :( D B) then f(?) = : : : : a) :? A ? b) :? D ? c) ? A ? 9: .) ? D ? 9: 141414.If14.If f(?) = A is analytic I = :B then f(?) = U : : a) ? A b) ? A c) ? A .) ? D ? 9: : : : : 151515.15. If f(?) = Q A B D :BR A Q DB A :BR is analytic ,then the mmaluealue of a, b are respectuallyrespectually a) ppp1,1p1,1 b) ppp1,2p1,2 c) 1,1,pppp11 c) 2,2,pppp1111 : : 161616.16. If f(?) = Q DB RA BA is .ifferentiable at emery point ,the constants a) 2b=a b) 4b=a cc)) 2a=b .) a=b : : 171717.17. If = : A D B is harmonic , then the malue of m is a) 3 b) 2 c) 0 .) 1 ? 181818.18. If the function f(?) = K? , A = : : : : B KB K B KB B : a) :KB: D :KB: b) (K):KB: A (K):KB: c) (K):KB: A (K):KB: .) Q A ZR A •B 191919.Any19.Any two harmonic conjugates of a gimen harmonic function u(2,y) .iffer by a) 2 b) y c) 2y .) constant 202020.20. The image of the strip 0<2<1 un.er the transfortransformationmation w=il is a) W < < 1 b) W < < 1 c) < < 2 .) < < 2 vw! cB 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 d ( h f !_ ) ? 111.1. The ra.ius of conmergence of `!b isisis a) b) c) 9 .) 222.2. The ra.ius of conmergence of `Kb ? isisis a) b) c) 9 .) K 333.3. The ra.ius of conmergence of `(K:)(Kd)b ? isisis a) b) c) 9 .) : ! 444.4. The ra.ius of conmergence of `:!b ? isisis a) b) c) 9 .) U (a) 555.5. The ra.ius of conmergence of ` b (? D :) isisis a) b) c) 9 .) 666.6. The ra.ius of conmergence of (d A U)? isisis a) b) c) 9Z .) U : 777.7. The ra.ius of conmergence of ` A b isisis a) b) c) 9 .) W ?aZ 888.The8.The inmariants points of w = ?a• isisis a) 3,3,pppp55 b) 3,3,pppp33 c) 3,5 .) ppp3,p3,3,3,pppp5555 d?aU 999.The9.The inmariants points of w = ?a isisis a) :, D: b) W, c) ± .) ±d ? 101010.The10.The inmariants pointpointss of w = :a? isisis a) :, D: b) W, c) ± .) ±d ?a 111111.The11.The inmariants points of w = ?K isisis a) :, D: b) W, c) ± .) ±d ? 11121222.The.The inmariants points of w = :?a isisis 5 a) :, D: b) W, c) ± .) ±d d?aZ 131313.The13.The inmariants points of w = ?K isisis a) :, D: b) W, c) ± : .) ±d ?K 141414.The14.The inmariants points of w = :?K isisis a) ± ]: b) ± ]d c) ± : .) ± d 151515.The15.The transformation w = ? A is sai. to be a) Translation b) Magnification c) Rotation .) Inmersion 161616.The16.The transformation w = ? is sai. to be a) Translation b) Magnification III Rotation ccc)c) Inmersion .) none 171717.The17.The transformation w = 9? is sai. to be a) Translation b) Magnification c) Rotation .) Inmersion I Reflection 181818.The18.The curme I their images un.er w = 9? are gimen below , state which of the following is truetrue 1) Circle not throu 0 into circle not throu 0 2) St. line not throu 0 into circle throu 0 3) Circle throu 0 into St.line not throu 0 4) St.line throu 0 into St.line throu 0 a) 1,2,3 b) 2,3,4 c) 1,2,3,4 .) 3,4 : 191919.The19.The angle of rotatirotationon at l = 1Ai un.er the map w = isisis a) 45 b) 0 c)c) 90 .) 180 20.The image of the circle J? D dJ =un.erun.er the map d w = 9? isisis a) circle b) st.line c) square .) rectangle vw! cB 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 U ( !f! I •••‘’ “”•‘–‘—•“•”) 111.1.
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