DEMOIVRE's THEOREM

Question

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.
(3 − 2i)^8

Answer 1

zⁿ = rⁿ [cos(nθ) + i sin(nθ)] = rⁿcos(nθ) + irⁿsin(nθ)

 

r = √[3² + (-2)²]

 

Note the phase angle is in quadrant IV.

 

θ = arctan(-2/3) ≅ 326.31°

 

n = 8

 

Plug in the numbers and finish from here.