Transcript (RECTANGULAR TO TRIGONOMETRIC FORM)

Trigonometric form of
COMPLEX NUMBER
Grab your book and calculator
•Until now, you have always been told
that you can’t take the square root of a
negative number. If you use imaginary
units, you can!
•The imaginary unit is ¡.
•¡=
•It is used to write the square root of a
negative number.
Imaginary Unit
The Complex plane
Real Axis
Imaginary Axis
Graphing in the complex plane
Absolute Value of a Complex
Number
• The distance the complex number is
from the origin on the complex
plane.
• If you have a complex number
• the absolute value can be found
using:
Examples
• 1.
2.
Which of these 2 complex numbers is closest
to the origin?
-2+5i
The Trig form of a Complex Number
Converting from Rectangular form to
Trig form
Convert z = 4 + 3i to trig form.
1. Find r
2. Find
3. Fill in the blanks
Practice
Given: 3 - 5i
A. Graph the complex number
B. Find its absolute value
C. Convert from complex form to
trigonometric form
Warm-up
Convert the following complex numbers to its polar
form
3-3i
4 - 4√3i
3 + √3i
4i
7
2√2 - i