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

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

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

4. Convert 1 - i to Trig(Polar) Form

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

6. Convert 3 - 4i to Trig(Polar) Form

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

8. Convert to Standard Form

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

10. Multiplication of Complex Numbers in Trig(Polar) Form

11. Division of Complex Numbers in Trig(Polar) Form

12. Division of Complex Numbers in Trig(Polar) Form

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

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

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

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

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

19. Find the 3 cube roots of -8

21. Find the 4 roots of 3 - 4i

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