Trig (Polar) Form of a Complex Number By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: February 23, 2011

Absolute Value of a Complex Number The distance from the origin to the point (a, b). a

Trig (Polar) form of a Complex Number (a, b) r b a

Convert 1 - i to Trig(Polar) Form

Convert -1 + i to Trig(Polar) Form Select the correct Quadrant

Convert 3 - 4i to Trig(Polar) Form

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

Convert to Standard Form

Multiplication of Complex Numbers in Trig(Polar) Form -1

Multiplication of Complex Numbers in Trig(Polar) Form

Division of Complex Numbers in Trig(Polar) Form

Division of Complex Numbers in Trig(Polar) Form

Powers of Complex Numbers in Trig(Polar) Form This is called DeMoivre’s Theorem

Use DeMoivre’s Thm to evaluate: Convert to trig form:

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

Roots of Complex Numbers in Trig(Polar) Form DeMoivre’s Theorem will help us with this

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

Find the 3 cube roots of -8

Find the 4 roots of 3 - 4i

Find the 15 roots of 4 - 7i Just Kidding!!!!!