Question

Use De Moivre's theorem to write the complex number in trigonometric form.

Answer 1

Answer:

C is the correct answer

Step-by-step explanation:

the amplitude is multiplied by the power and the magnitude is raised to that power

Answer 2

$\bf \qquad \textit{power of two complex numbers} \\\\\ [\quad r[cos(\theta)+isin(\theta)]\quad ]^n\implies r^n[cos(n\cdot \theta)+isin(n\cdot \theta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left[cos\left( \frac{\pi }{4} \right)+i~sin\left( \frac{\pi }{4} \right) \right]^3 \implies \left[1\left[ cos\left( \frac{\pi }{4} \right)+i~sin\left( \frac{\pi }{4} \right) \right] \right]^3$

$\bf 1^3\left[cos\left( 3\cdot \frac{\pi }{4} \right) +i~sin\left( 3\cdot \frac{\pi }{4} \right) \right]\implies 1\left[ cos\left( \frac{3\pi }{4} \right)+i~sin\left( \frac{3\pi }{4} \right) \right] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cos\left( \frac{3\pi }{4} \right)+i~sin\left( \frac{3\pi }{4} \right)~\hfill$