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**Trig (Polar) Form of a Complex Number**

By: Jeffrey Bivin Lake Zurich High School Last Updated: February 23, 2011

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**Absolute Value of a Complex Number**

The distance from the origin to the point (a, b). a

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**Trig (Polar) form of a Complex Number**

(a, b) r b a

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**Convert 1 - i to Trig(Polar) Form**

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**Convert -1 + i to Trig(Polar) Form**

Select the correct Quadrant

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**Convert 3 - 4i to Trig(Polar) Form**

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**Convert 5(cosπ + i·sinπ ) to Standard Form**

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**Convert to Standard Form**

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**Multiplication of Complex Numbers in Trig(Polar) Form**

-1

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**Multiplication of Complex Numbers in Trig(Polar) Form**

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**Division of Complex Numbers in Trig(Polar) Form**

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**Division of Complex Numbers in Trig(Polar) Form**

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**Powers of Complex Numbers in Trig(Polar) Form**

This is called DeMoivre’s Theorem

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**Use DeMoivre’s Thm to evaluate:**

Convert to trig form:

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Solve: x6 – 1 = 0 Just for Fun This one worked nicely because the equation was factorable. What happens if it isn’t nicely factorable?

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**Roots of Complex Numbers in Trig(Polar) Form**

DeMoivre’s Theorem will help us with this

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Find the 6 roots of 1 i.e. x6 = 1

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Find the 3 cube roots of -8

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Find the 4 roots of 3 - 4i

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Find the 15 roots of i Just Kidding!!!!!

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Lake Zurich High School

Lake Zurich High School

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