Question

In Problems 10–12, perform the given operation, where $z=2\left(\cos 85°+i\sin 85°\right)$and $w=3\left(\cos 22°+i\sin 22°\right)$. Write your answer in polar form.

$w^5$

Short answer

The answer is$243\left(\cos 110°+i\sin 110°\right)$

Step-by-step solution

Step 1. Given information

We have been given $z=2\left(\cos 85°+i\sin 85°\right)$and $w=3\left(\cos 22°+i\sin 22°\right)$.

We have to perform the operation$w^5$

Step 2. Perform the operation

$$\begin{gathered} w^5 \\ =3^5\left(\cos \left(5\times 22°\right)+i\sin \left(5\times 22°\right)\right) \\ =243\left(\cos 110°+i\sin 110°\right) \end{gathered}$$