Section 6.6 – Complex Numbers DeMoivre’s Theorem and n th Roots

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# Section 6.6 – Complex Numbers DeMoivre’s Theorem and n th Roots - PowerPoint PPT Presentation

Section 6.6 – Complex Numbers DeMoivre’s Theorem and n th Roots. IMAGINARY NUMBERS and the COMPLEX PLANE. Imaginary axis. Real Part. Imaginary Part. Real axis. TRIGONMETRIC FORM of a COMPLEX NUMBER. PRODUCTS and QUOTIENTS of COMPLEX NUMBERS in TRIGONOMETRIC FORM. DeMoirve’s Theorem.

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### Section 6.6 – Complex NumbersDeMoivre’s Theorem and nth Roots

IMAGINARY NUMBERS and the COMPLEX PLANE

Imaginary axis

Real Part

Imaginary Part

Real axis

DeMoirve’s Theorem

So, writing the complex number in

It’s trigonometric form, we get…

A complex number has n distinct nth roots

(i.e. 3 distinct 3rd, or cube, roots, and 5 distinct 5th roots, etc… )

a + bi

Imaginary axis

2i

i

Real axis

-i

-2i