Question

Can you help me and answer it like the paper says

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for the polar form of the given complex number

`\begin{gathered} z=r\cos \theta \\ \text{where r is the radius} \\ \theta\text{ is the measure of angle in radians} \\ \text{Note that:} \\ \pi=180^(\circ) \end{gathered}`

STEP 2: Complete the table by substituting and solving for the unknown

`\begin{gathered} z=r\cos \theta\Rightarrow r\cos \pi \\ To\text{ get }\theta\text{ in row 1} \\ r=3,\pi=180 \\ z=3\cos 180 \\ \\ To\text{ get r and }\theta\text{ in row }2 \\ z=rcis\theta\Rightarrow(1)/(2)cis2\pi \\ By\text{ comparison,} \\ r=(1)/(2),\theta=2\pi=2*180^(\circ)=360^(\circ) \\ \\ To\text{ get r and }\theta\text{ in row }3 \\ z=rcis\theta\Rightarrow cis(\pi)/(4) \\ By\text{ comparison,} \\ r=2,\theta=(\pi)/(4) \\ \\ To\text{ get r and }\theta\text{ in row }4 \\ z=rcis\theta\Rightarrow cis(\pi)/(2) \\ By\text{ comparison,} \\ r=1,\theta=(\pi)/(2) \end{gathered}`

STEP 3: Complete the table