Question

Convert z=6cis (pi) I sent a picture of the question and the multiple choice answerssss

Answer 1

We have the angle in polar form:

$z=6\text{cis}(\pi)$

It's an abreviature of:

$z=6(\cos \pi+i\sin \pi)$

Then, we have to calculate cos(pi) and sin(pi)

We know by the unit circle that:

$\begin{gathered} \cos (\pi)=-1 \\ \sin (\pi)=0 \end{gathered}$

Then we can replace:

$\begin{gathered} z=6(-1+i\cdot0) \\ z=-6 \end{gathered}$

The correct answer is z = -6, which is the first option