Modulus-argument form Problem set B Answers

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

1. (a) \(r = 17,\ \theta = -0.490\)
2. (b) \(r = 5.83,\ \theta = 2.60\)

1. (a) \(5 \sqrt{3} + 5i\)
2. (b) \(- 2 \sqrt{2} + 2 \sqrt{2}i\)
3. (c) \(4.08 - 8.02i\)

1. (a) \(9\,\text{cis}\left(-\dfrac{\pi}{8}\right)\)
2. (b) \(2\,\text{cis}\left(\dfrac{3\pi}{4}\right)\)
3. (c) \(6\,\text{cis}\left(\dfrac{3\pi}{4}\right)\)

1. (a) \(-\dfrac{\pi}{4}\) (\(-0.785\))
2. (b) \(35.4 - 35.4i\)
3. (c) Distance 10 m, argument \(2.50\)

\(5\,\text{cis}\,\dfrac{5\pi}{4}\)

\(4\,\text{cis}\left(-\dfrac{2\pi}{7}\right)\)

1. (a) \(-5\sqrt{3} + 5i\)
2. (b) \(-5\sqrt{3} - 5i\); \(10\,\text{cis}\left(-\dfrac{5\pi}{6}\right)\)
3. (c) 10