Find zw and StartFraction z Over w EndFraction

Question

. Write each answer in polar form and in exponential form.
z
equals3 left parenthesis cosine StartFraction 2 pi Over 9 EndFraction plus i sine StartFraction 2 pi Over 9 EndFraction right parenthesis
w
equals12 left parenthesis cosine StartFraction pi Over 9 EndFraction plus i sine StartFraction pi Over 9 EndFraction right parenthesis
Question content area bottom
Part 1
The product zw in polar form is
  
enter your response here and in exponential form is
  
enter your response here.
​(Simplify your answer. Type an exact​ answer, using pi as needed. Use integers or fractions for any numbers in the​ expression.)

Answer 1

Part 1:
The product zw in polar form is 36(cos(2π/9 + π/9) + i sin(2π/9 + π/9)) = 36(cos(3π/9) + i sin(3π/9)) = 36(cos(π/3) + i sin(π/3)) = 36(cos(60°) + i sin(60°)) = 36(cos(60°) + i sin(60°)) = 36(cos(60°) + i sin(60°)) = 36(cos(60°) + i sin(60°))

In exponential form, the answer is 36e^(iπ/3)