Find zw and StartFraction z Over w EndFraction
. 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.)
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)