Question

Convert to rectangular form.

Answer 1

-16 sqrt(3) +16i

Explanation:

z = 2 cis (pi/6)

z^5 = 2^5 cis (5*pi/6)

z^5 = 32 cis (5pi/6)

z^5 = 32 cos (5pi/6) + 32 i sin (5pi/6)

= 32 * (-sqrt(3)/2) + 32i (1/2)

= -16 sqrt(3) +16i