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IB Mathematics: Applications and Interpretation HL · AHL 6: Complex Numbers · AHL 6.8

Exponential form Problem set B Answers

Skills

    1. (a) \(zw = 24e^{i\frac{\pi}{2}}\)
    2. (b) \(zw = 12e^{i\frac{5\pi}{6}}\)
    3. (c) \(zw = 2e^{i\frac{5\pi}{12}}\)
    1. (a) \(\dfrac{z}{w} = 4e^{i\frac{5\pi}{12}}\)
    2. (b) \(\dfrac{z}{w} = 1.75e^{i\frac{3\pi}{2}}\)
    3. (c) \(\dfrac{z}{w} = 7e^{i\frac{7\pi}{4}}\)
    1. (a) \(z = \sqrt{2}e^{i\frac{3\pi}{4}},\ w = 2e^{i\frac{\pi}{3}}\)
    2. (b) \(zw = 2\sqrt{2}e^{i\frac{13\pi}{12}},\ \dfrac{z}{w} = \dfrac{\sqrt{2}}{2}e^{i\frac{5\pi}{12}}\)
    1. (a) \(z^* = 5e^{i\frac{5\pi}{6}}\)
    2. (b) \(zz^* = 25\)
    3. (c) \(z^* = -\frac{5\sqrt{3}}{2} + \frac{5}{2}i\)
    1. (a) \(z_{\pi/2} = 0.393i,\ z_{\pi} = -0.785,\ z_{3\pi/2} = -1.18i\)
    2. (b) \(\theta = 12,\ z = 2.53 - 1.61i\)

In context

    1. (a) \(T = 8e^{i\frac{7\pi}{12}}\)
    2. (b) \(T' = 6e^{i\frac{23\pi}{12}}\)

Stretch

    1. (a) \(\dfrac{1}{z} = 0.125e^{i\frac{5\pi}{3}}\)
    2. (b) \(\dfrac{z}{z^*} = e^{i\frac{8\pi}{5}}\)

jmaths.xyz · AI HL · AHL 6.8 Exponential form