The Complex Plane; De Moivre’s Theorem. Polar Form.

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Presentation transcript:

The Complex Plane; De Moivre’s Theorem

Polar Form

1. Plot each complex number in the complex plane and write it in polar form. Express the argument in degrees (Similar to p.334 #11-22)

2. Plot each complex number in the complex plane and write it in polar form. Express the argument in degrees (Similar to p.334 #11-22)

3. Plot each complex number in the complex plane and write it in polar form. Express the argument in degrees (Similar to p.334 #11-22)

4. Write each complex number in rectangular form (Similar to p.334 #23-32)

5. Write each complex number in rectangular form (Similar to p.334 #23-32)

6. Write each complex number in rectangular form (Similar to p.334 #23-32)

Multiplication and Division

7. Find zw and z/w. Leave your answers in polar form (Similar to p.334 #33-40)

8. Find zw and z/w. Leave your answers in polar form (Similar to p.334 #33-40)

9. Find zw and z/w. Leave your answers in polar form (Similar to p.334 #33-40)

10. Write each expression in the standard form a + bi (Similar to p.334 #41-52)

11. Write each expression in the standard form a + bi (Similar to p.334 #41-52)

Let w = r(cos θ o + i sin θ o be a complex number, and let n > 2 be an integer. There are n distinct complex nth roots given by:

12. Find all the complex roots. Leave your answers in polar form with the argument in degrees (Similar to p.335 #53-60)

13. Solve the following equation. Leave your answers in polar form with the argument in degrees (Similar to p.335 #53-60)

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