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

Exponential form Problem set A Answers

Skills

    1. (a) \(zw = 15e^{i\frac{\pi}{3}}\)
    2. (b) \(zw = 14e^{i\frac{19\pi}{12}}\)
    3. (c) \(zw = 6e^{i\frac{5\pi}{12}}\)
    1. (a) \(\dfrac{z}{w} = 4e^{i\frac{\pi}{2}}\)
    2. (b) \(\dfrac{z}{w} = 2.5e^{i\frac{3\pi}{2}}\)
    3. (c) \(\dfrac{z}{w} = 3e^{i\frac{4\pi}{3}}\)
    1. (a) \(z = \sqrt{2}e^{i\frac{\pi}{4}},\ w = 2e^{i\frac{\pi}{6}}\)
    2. (b) \(zw = 2\sqrt{2}e^{i\frac{5\pi}{12}},\ \dfrac{z}{w} = \dfrac{\sqrt{2}}{2}e^{i\frac{\pi}{12}}\)
    1. (a) \(z^* = 3e^{i\frac{3\pi}{4}}\)
    2. (b) \(zz^* = 9\)
    3. (c) \(z^* = -\frac{3\sqrt{2}}{2} + \frac{3\sqrt{2}}{2}i\)
    1. (a) \(z_{\pi/2} = 0.785i,\ z_{\pi} = -1.57,\ z_{3\pi/2} = -2.36i\)
    2. (b) \(\theta = 8,\ z = -0.582 + 3.96i\)

In context

    1. (a) \(I = 8e^{i\frac{\pi}{12}}\)
    2. (b) \(I' = 6e^{i\frac{3\pi}{2}}\)

Stretch

    1. (a) \(\dfrac{1}{z} = \frac{1}{6}e^{i\frac{7\pi}{4}}\)
    2. (b) \(\dfrac{z}{z^*} = e^{i\frac{4\pi}{3}}\)

jmaths.xyz · AI HL · AHL 6.8 Exponential form