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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 A Answers

Skills

    1. (a) \(z^{4} = \frac{81}{2}+\frac{81 \sqrt{3}}{2}i\)
    2. (b) \(z^{3} = -4+4 \sqrt{3}i\)
    3. (c) \(z^{4} = 4i\)
    1. (a) \(z^{4} = -8+8 \sqrt{3}i\)
    2. (b) \(z^{6} = 8i\)
    3. (c) \(z^{4} = -64\)
    1. (a) \(u_2 = 6 + 8i,\ u_3 = -1.4 + 4.8i\)
    2. (b) \(|r| = 0.5\)
    3. (c) \(40\)

In context

    1. (a) \(m^4 \approx 1.04 + 1.80i\)
    2. (b) 2.07 cm

Stretch

    1. (a) \(z = 2e^{i\frac{\pi}{3}}\)
    2. (b) \(n = 3,\ z^3 = -8\)

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