Trig form of Complex Numbers

1. Trig form of Complex Numbers • Warm-Up: Do the following operations: • (3 + 5i) + (4 – 2i) b) (3 + 5i)(4 – 2i) Objective: Be able to operate with complex numbers, and be able to convert complex numbers into Trig Form and vise versa. TS: Examining information from more than one view point.

2. Complex Numbers a+bi where i=√-1 (i2 = -1) Remember: They can be graphed on complex plane Imaginary axis 3 + 2i 1 Real axis 1

3. Absolute Value • Absolute value is the _________________ So |a + bi| = Find |-3 + 4i| |-2 – 6i| Imaginary 1 Real 1

4. Trig form of Complex Numbers To effectively work with powers and roots, it is helpful to use trig to express imaginary numbers. If θis the angle formed to point (a, b) then a = r cos θ & b = r sin θ Thusa + bi = (r cos θ) + (r sin θ) I = r cis θ where r = (r is called themodulus) and (θis called theargument) Imaginary r b θ Real a

5. Switching Between Forms Write each in trigonometric form • 2 + 2i 2) -1 – √3i

6. Switching Between Forms Write each in trigonometric form 3) 2.5(√3 – i) 4) 7

7. Switching Between Forms Write each in trigonometric form 5) 1 + 2i

8. Switching Between Forms Write each in standard form • 5(cos135° + i sin135°) 2) ¾ cis 330°

9. Switching Between Forms Write each in standard form 3) 4)

10. You Try Represent 4 – 4√3i graphically, and find the trigonometric form of a number. Also find the absolute value of it. Click here for answers

11. Imaginary Real Click here for Question 4 – 4√3i