Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-hl/complex-numbers/ahl-6-7/problems/

jmaths

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

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

Skills

    1. (a) \(zw = 12\,\text{cis}\left(\frac{3\pi}{7}\right)\)
    2. (b) \(zw = 15\,\text{cis}\left(\frac{5\pi}{4}\right)\)
    3. (c) \(zw = 10\,\text{cis}\left(\frac{\pi}{3}\right)\)
    1. (a) \(\dfrac{z}{w} = 4\,\text{cis}\left(\frac{\pi}{2}\right)\)
    2. (b) \(\dfrac{z}{w} = 3.5\,\text{cis}\left(\frac{19\pi}{12}\right)\)
    1. (a) \(z^3 = 8\,\text{cis}\left(\frac{\pi}{3}\right)\)
    2. (b) \(z^4 = 81\,\text{cis}\left(\frac{4\pi}{3}\right)\)
    1. (a) \(\dfrac{z^2}{w^3} = \frac{3 \sqrt{3}}{2}+\frac{3}{2}i\)
    2. (b) \(\dfrac{z^3}{w^2} = 2i\)

In context

    1. (a) \(FV = 6\,\text{cis}\left(\frac{23\pi}{12}\right)\)
    2. (b) \(VF^2 = 3\,\text{cis}\left(\frac{5\pi}{3}\right)\): amplitude 3 volts, phase \(\frac{5\pi}{3}\)

Stretch

    1. (a) \(n = 8\), \(z^8 = -256\)
    2. (b) \(z = 10\,\text{cis}\left(\frac{\pi}{2}\right),\ w = 2\,\text{cis}\left(\frac{\pi}{3}\right)\)

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