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### Course: Precalculus>Unit 3

Lesson 8: Multiplying and dividing complex numbers in polar form

# Taking and visualizing powers of a complex number

Given a complex number in rectangular form, we can convert it to polar form to show how to visualize powers of the complex number by scaling and rotating it by its own modulus and argument. Created by Sal Khan.

## Want to join the conversation?

• That's the De Moivre's theorem isnt it
• Yes, that's correct! De Moivre's theorem states that for any complex number z and any positive integer n, (cos θ + i sin θ)^n = cos nθ + i sin nθ. It is a useful tool for raising complex numbers to powers and expressing them in polar form.
• Can we apply polar form to real numbers as well?
• Yes, the angle would be 0 for positive numbers and 180 for negative numbers. Example: -5=5(cos(180)+isin(180)). The imaginary component will disappear because sin(180) and sin(0) are both 0.