Question

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

Answer 1

C. 27i

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