Use DeMoivre's Theorem to find (3cis (pi/6)) ^3.

a.) (27sqrt3) / 2 + 27/2 i

b.) (9sqrt3) / 2 + 9/2 i

c.) 27i

d.) 9i

C. 27i

Step-by-step explanation:

Given the complex number in polar coordinate expressed as

z = r (cos∅+isin∅)

zⁿ = {r (cos∅+isin∅) }ⁿ

According to DeMoivre's Theorem;

zⁿ = rⁿ (cosn∅+isinn∅)

Given the complex number;

(3cis (pi/6)) ^3

= {3 (cosπ/6 + isinπ/6) }^3

Using DeMoivre's Theorem;

= 3³ (cos3π/6 + isin3π/6)

= 3³ (cosπ/2 + isinπ/2)

= 3³ (0 + i (1))

= 27i

The right answer is 27i