1. Number and Algebra

De Moivre’s Theorem — Quiz

Test your understanding of de moivre’s theorem with 5 practice questions.

Practice Questions

Question 1

What is the main idea of De Moivre’s Theorem for a complex number written in polar form as $z=r(\cos\theta+i\sin\theta)$?

Question 2

If $z=\cos 30^\circ+i\sin 30^\circ$, what is $z^3$?

Question 3

A complex number is written as $z=2(\cos 45^\circ+i\sin 45^\circ)$. What is the modulus of $z^4$?

Question 4

Which expression is equivalent to $\left(\cos\theta+i\sin\theta\right)^5$?

Question 5

If $z=\cos 60^\circ+i\sin 60^\circ$, what is the argument of $z^2$?