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8.3 Polar Form of Complex Numbers; De Moivre’s Theorem

Focus on de moivre modulus and multiply polar moduli.

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01Modulus and polar form of a complex numberWorked steps · five questions 02Multiplying and dividing in polar formWorked steps · five questions 03De Moivre's Theorem (powers)Worked steps · five questions 04nth roots of complex numbersWorked steps · five questions

Lesson brief and rules

8.3 Polar Form of Complex Numbers; De Moivre’s Theorem

$[r(\cos \theta +i \sin \theta )]^{n}=r^{n}(\cos n\theta +i \sin n\theta )$ .

Worked example

1

01 / If

z=4(\cos \theta +i \sin \theta )

, find the modulus of

z^{3}

02 / The modulus raises to the third power:

4^{3}=64

03 / Answer:

64

Worked example 2 · Multiply polar moduli

If $|z|=4$ and $|w|=6$ , find $|$ zw $|$ .

The modulus of a product is the product of moduli. Answer: $24$

15 questions covering every idea, with a worked answer for each.Start practice ↗

Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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8.3 Polar Form of Complex Numbers; De Moivre’s Theorem

Ideas in this lesson

8.3 Polar Form of Complex Numbers; De Moivre’s Theorem