Trig form of Complex Numbers 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. Warm-Up: Do the following operations: a)(3 + 5i) + (4 – 2i)b) (3 + 5i)(4 – 2i)

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

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

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

Switching Between Forms Write each in trigonometric form 1)2 + 2i2) -1 – √3i

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

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

Switching Between Forms Write each in standard form 1)5(cos135° + i sin135°) 2) ¾ cis 330°

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

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

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