PC­­Lesson 6­5(a)_notes.notebook January 15, 2016

6.5(a) Trigonometric Form of a Complex Number

Students will be able to . . .

• plot complex numbers in the complex plane and find absolute values of complex numbers.

• write trigonometric forms of complex numbers.

• write the standard form of complex numbers.

• multiply and divide complex numbers written in trigonometric form.

Complex Plane

Real Axis

Imaginary Axis

Example #1

Plot z = 3 ‐ 4 i and find its absolute value.

Absolute value of the complex number z = a + bi is given by

a + bi = a2 + b2

PC­­Lesson 6­5(a)_notes.notebook January 15, 2016

Trigonometric Form of a Complex Number

Reminder ‐‐ Use a calculator to find θ when the angle is not an angle on the unit circle. Remember when using a calculator to find θ, θ will be between ‐π/2 and π/2. Pay attention to which quadrant the complex number is in. Write the trigonometric from of the complex number using radians.

Complex number ­­­­ z = a + bi

Trigonometric form of the complex number

z = r (cos θ + sin θi )

r is the modulus of z

θ is the argument of z

PC­­Lesson 6­5(a)_notes.notebook January 15, 2016

Example #2

Write the complex number in trigonometric form without using a calculator.

(c)

(a)

(b)

PC­­Lesson 6­5(a)_notes.notebook January 15, 2016

Example #3

Represent the complex number graphically and find the trigonometric form of the number.

(a) (b)

(c) (d)

Homework P452: 15­39(odd)