Question

1. Let \(z = 3\operatorname{cis}2\). What is the imaginary part of \(z\) rounded to 5 decimal places?

   The answer is \(2.72789\).

   The imaginary part is given by \(3 \sin 2 = 2.72789228\ldots \approx 2.72789\).

2. Let \(z = -1 - \sqrt{3}i\). Which of the following is the polar form of \(z\)?

   1. \(4 \operatorname{cis} \frac{4\pi}{3}\)

   2. \(2 \operatorname{cis} \frac{\pi}{3}\)

   3. \(2 \operatorname{cis} \frac{4\pi}{3}\)

   The answer is C.