SOLUTION
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
[tex]\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}[/tex]
STEP 2: Complete the table by substituting and solving for the unknown
[tex]\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\frac{1}{2}cis2\pi \\ By\text{ comparison,} \\ r=\frac{1}{2},\theta=2\pi=2\times180^{\circ}=360^{\circ} \\ \\ To\text{ get r and }\theta\text{ in row }3 \\ z=rcis\theta\Rightarrow cis\frac{\pi}{4} \\ By\text{ comparison,} \\ r=2,\theta=\frac{\pi}{4} \\ \\ To\text{ get r and }\theta\text{ in row }4 \\ z=rcis\theta\Rightarrow cis\frac{\pi}{2} \\ By\text{ comparison,} \\ r=1,\theta=\frac{\pi}{2} \end{gathered}[/tex]
STEP 3: Complete the table
