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IB Mathematics: Applications and Interpretation HL · AHL 6: Complex Numbers · AHL 6.9

Powers and de Moivre's formula Problem set B Answers

Skills

    1. (a) \(z^{5} = 16+16 \sqrt{3}i\)
    2. (b) \(z^{3} = -32 \sqrt{2}+32 \sqrt{2}i\)
    3. (c) \(z^{4} = -\frac{9}{2}+\frac{9 \sqrt{3}}{2}i\)
    1. (a) \(z^{3} = 8i\)
    2. (b) \(z^{6} = -512i\)
    3. (c) \(z^{2} = -8-8 \sqrt{3}i\)
    1. (a) \(u_2 = -7.2 + 9.6i,\ u_3 = -2.52 - 8.64i\)
    2. (b) \(|r| = 0.75\)
    3. (c) \(64\)

In context

    1. (a) \(m^3 \approx 0.256 + 0.443i\)
    2. (b) 0.512 cm

Stretch

    1. (a) \(z = \sqrt{2}e^{i\frac{7\pi}{4}}\)
    2. (b) \(n = 4,\ z^4 = -4\)

jmaths.xyz · AI HL · AHL 6.9 Powers and de Moivre's formula