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Jeff Bivin -- LZHS Trig (Polar) Form of a Complex Number By: Jeffrey Bivin Lake Zurich High School Last Updated: February 23, 2011.

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Presentation on theme: "Jeff Bivin -- LZHS Trig (Polar) Form of a Complex Number By: Jeffrey Bivin Lake Zurich High School Last Updated: February 23, 2011."— Presentation transcript:

1 Jeff Bivin -- LZHS Trig (Polar) Form of a Complex Number By: Jeffrey Bivin Lake Zurich High School Last Updated: February 23, 2011

2 Jeff Bivin -- LZHS Absolute Value of a Complex Number The distance from the origin to the point (a, b). (a, b) a b

3 Jeff Bivin -- LZHS Trig (Polar) form of a Complex Number (a, b) a r b

4 Jeff Bivin -- LZHS Convert 1 - i to Trig(Polar) Form

5 Jeff Bivin -- LZHS Convert -1 + i to Trig(Polar) Form Select the correct Quadrant

6 Jeff Bivin -- LZHS Convert 3 - 4i to Trig(Polar) Form

7 Jeff Bivin -- LZHS Convert 5(cosπ + i·sinπ ) to Standard Form

8 Jeff Bivin -- LZHS Convert to Standard Form

9 Jeff Bivin -- LZHS Multiplication of Complex Numbers in Trig(Polar) Form

10 Jeff Bivin -- LZHS Multiplication of Complex Numbers in Trig(Polar) Form

11 Jeff Bivin -- LZHS Division of Complex Numbers in Trig(Polar) Form

12 Jeff Bivin -- LZHS Division of Complex Numbers in Trig(Polar) Form

13 Jeff Bivin -- LZHS Powers of Complex Numbers in Trig(Polar) Form This is called DeMoivres Theorem

14 Jeff Bivin -- LZHS Use DeMoivres Thm to evaluate: Convert to trig form:

15 Jeff Bivin -- LZHS Solve: x 6 – 1 = 0 This one worked nicely because the equation was factorable. What happens if it isnt nicely factorable? Just for Fun

16 Jeff Bivin -- LZHS Roots of Complex Numbers in Trig(Polar) Form DeMoivres Theorem will help us with this

17 Jeff Bivin -- LZHS Find the 6 roots of 1 i.e. x 6 = 1

18 Jeff Bivin -- LZHS

19 Find the 3 cube roots of -8

20 Jeff Bivin -- LZHS

21 Find the 4 roots of 3 - 4i

22 Jeff Bivin -- LZHS

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


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