Modulus-argument form Problem set A Answers

1. (a) \(2\,\text{cis}\left(\dfrac{\pi}{3}\right)\)
2. (b) \(4 \sqrt{2}\,\text{cis}\left(\dfrac{3\pi}{4}\right)\)
3. (c) \(2\,\text{cis}\left(\dfrac{7\pi}{6}\right)\)
4. (d) \(3 \sqrt{2}\,\text{cis}\left(\dfrac{7\pi}{4}\right)\)

1. (a) \(r = 13,\ \theta = -1.18\)
2. (b) \(r = 7.28,\ \theta = 2.86\)

1. (a) \(4 + 4 \sqrt{3}i\)
2. (b) \(- 3 \sqrt{3} + 3i\)
3. (c) \(-4.66 + 5.22i\)

1. (a) \(6\,\text{cis}\left(-\dfrac{2\pi}{9}\right)\)
2. (b) \(4\,\text{cis}\left(-\dfrac{5\pi}{6}\right)\)
3. (c) \(3\,\text{cis}\left(\dfrac{2\pi}{3}\right)\)

1. (a) \(\dfrac{\pi}{6}\) (0.524)
2. (b) \(6.93 + 4i\)
3. (c) Distance 13 km, argument \(-1.18\)

\(2\,\text{cis}\,\dfrac{7\pi}{6}\)

\(3\,\text{cis}\left(-\dfrac{\pi}{5}\right)\)

1. (a) \(-3 + 3\sqrt{3}\,i\)
2. (b) \(-3 - 3\sqrt{3}\,i\); \(6\,\text{cis}\left(-\dfrac{2\pi}{3}\right)\)
3. (c) \(6\sqrt{3} = 10.4\)