<p>Maths Quest Maths C Year 11 for Queensland Chapter 2 Number systems: complex numbers WorkSHEET 2.1 1</p><p>WorkSHEET 2.1 Number systems: complex numbers Name: ______</p><p>1 Plot the following complex numbers on the 6 same fully labelled Argand diagram. (a) A = 2 + 3i (b) B = –5 –i (c) C = 1 – 4i (d) D = –4 + 2i (e) E = 6i (f) F = –4</p><p>2 Perform the following operations using (a) 2z = 2(2 – 6i) = 4 – 12i 5 z = 2 – 6i w = –1 + 2i (b) w – z = –1 + 2i – (2 – 6i) x = 4 + i = –1 + 2i – 2 + 6i = –3 + 8i (a) 2z (c) 3x + 2w = 3(4 + i) + 2(–1 + 2i) (b) w – z = 12 + 3i –2 + 4i = 10 + 7i (c) 3x + 2w (d) x × w = (4 + i)(–1 + 2i) (d) x × w = –4 –i + 8i – 2 = –6 + 7i (e) z × w (e) z × w = (2 – 6i)(–1 + 2i) Plot the answers on the same Argand diagram. = –2 + 6i + 4i + 12 = 10 + 10i Maths Quest Maths C Year 11 for Queensland Chapter 2 Number systems: complex numbers WorkSHEET 2.1 2</p><p>3 Find the modulus of each of the following (a) z 22 (5)2 4 complex numbers: 4 25 (a) z = 2 – 5i 29 (b) w = –3 + 6i</p><p>(c) y = –6 + i (b) w (3)2 62 (d) x = 4 9 36 45 3 5</p><p>(c) y (6)2 12 36 1 37</p><p>(d) |x| = 4</p><p>4 Sketch the following complex numbers then 4 find the argument and principal argument of each:</p><p>(a) z = 1 – 4i</p><p>(b) w = –2 – 7i</p><p>(c) y = 3 + 4i</p><p>(d) x = –5i 4 (a) arg(z) tan 1 1 1.33 Arg(z) 1.33</p><p> 7 (b) arg(w) tan 1 2 1.29 Arg(w) 1.29 1.85 Maths Quest Maths C Year 11 for Queensland Chapter 2 Number systems: complex numbers WorkSHEET 2.1 3</p><p> 4 (c) arg(y) tan 1 3 0.64 Arg(y) 0.64</p><p>3 (d) arg(x) 2 Arg(x) 2</p><p>5 Sketch the following complex numbers and (a) 4 express them in polar form:</p><p>(a) z = 2 + 3i</p><p>(b) w = –4 –2i</p><p>(c) y = –3 + i z 22 32 4 9 13 3 (d) x = 5 – 5i arg(z) tan 1 0.98 (b) 2 z 13 cis 0.98</p><p> w (4) 2 (2) 2 16 4 20 2 5 2 arg(w) tan 1 0.46 4 Arg(w) 0.46 2.68 w 2 5 cis (2.68) (c)</p><p> y (3) 2 12 9 1 10 1 arg(y) tan 1 0.32 3 Arg(y) 0.32 2.82 y 10 cis 2.82 (d) Maths Quest Maths C Year 11 for Queensland Chapter 2 Number systems: complex numbers WorkSHEET 2.1 4</p><p> x 52 (5)2 25 25 50 5 2 5 arg(x) tan 1 5 4</p><p>6 Use common trigonometric ratios in their (a) 4 relevant triangles (but no formal calculator work) to express the following in polar form:</p><p>(a) z = 2 – 2i</p><p>(b) w = 1 3i z 2 2 cis (c) y = 4 3 4i 4 (b) (d) x = 5 5 i</p><p> 2 w 2 cis 3 (c)</p><p> y 8 cis 6 (d)</p><p>3 x 10 cis 4</p>
Details
-
File Typepdf
-
Upload Time-
-
Content LanguagesEnglish
-
Upload UserAnonymous/Not logged-in
-
File Pages4 Page
-
File Size-