pc--lesson 6-5(a) notes.notebook...pclesson 65(a)_notes.notebook january 15, 2016 6.5(a)...
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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)