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.

$z·w$

Short answer

The answer is$z·w=6\left(\cos 107°+i\sin 107°\right)$

Step-by-step solution

Step 1. Given information

We have been given $z=2\left(\cos 85°+i\sin 85°\right)$and localid="1646898828569" $w=3\left(\cos 22°+i\sin 22°\right)$.

We have to perform the operation$z·w$

Step 2. Perform the operation

$$\begin{gathered} z·w \\ =2\left(\cos 85°+i\sin 85°\right)\times 3\left(\cos 22°+i\sin 22°\right) \\ =6\left[\cos \left(85°+22°\right)+i\sin \left(85°+22°\right)\right] \\ =6\left(\cos 107°+i\sin 107°\right) \end{gathered}$$