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IB Mathematics: Applications and Interpretation HL · AHL 6: Complex Numbers · AHL 6.7

Products, quotients and powers in cis form Problem set B Answers

Skills

    1. (a) \(zw = 24\,\text{cis}\left(\frac{3\pi}{5}\right)\)
    2. (b) \(zw = 12\,\text{cis}\left(\frac{11\pi}{6}\right)\)
    3. (c) \(zw = 9\,\text{cis}\left(\frac{7\pi}{12}\right)\)
    1. (a) \(\dfrac{z}{w} = 5\,\text{cis}\left(\frac{\pi}{2}\right)\)
    2. (b) \(\dfrac{z}{w} = 1.5\,\text{cis}\left(\frac{17\pi}{12}\right)\)
    1. (a) \(z^5 = 243\,\text{cis}\left(\frac{\pi}{2}\right)\)
    2. (b) \(z^5 = 32\,\text{cis}\left(\frac{11\pi}{6}\right)\)
    1. (a) \(\dfrac{z^2}{w^3} = 4 \sqrt{2}+4 \sqrt{2}i\)
    2. (b) \(\dfrac{z^3}{w^2} = 1+\sqrt{3}i\)

In context

    1. (a) \(DS = 4\,\text{cis}\left(\frac{11\pi}{6}\right)\)
    2. (b) \(SD^3 = \text{cis}\left(\frac{7\pi}{6}\right)\): loudness 1, phase \(\frac{7\pi}{6}\)

Stretch

    1. (a) \(n = 6\), \(z^6 = -729\)
    2. (b) \(z = 6\,\text{cis}\left(\frac{5\pi}{6}\right),\ w = 3\,\text{cis}\left(\frac{\pi}{4}\right)\)

jmaths.xyz · AI HL · AHL 6.7 Products, quotients and powers in cis form