Day 1 Trig form of complex numbers
December 05, 2014
Review of Operations with Complex Numbers (in standard form)
Math Analysis AB ­ Unit 4B
(3 + 5i) + (4 ­ 2i)
Objective: Trig form of complex numbers
Thinking Skill: Explicitly assess information & draw conclusions
(3 + 5i) ­ (4 ­ 2i)
Warm Up: (3 + 5i)(4 ­ 2i)
1.) (3 + 5i) + (4 ­ 2i)
2.) (3+5i)(4 ­ 2i)
The complex conjugate of (3 + 5i) is __________
Definition of the Absolute Value of a Complex Number
The absolute value of the complex number z = a + bi is
Complex Numbers
|a + bi| = √a2 + b2
a + bi
real
It is the distance from the origin (0,0) to the point (a, b)
imaginary
Complex numbers can be graphed on a complex plane.
imaginary axis
real axis
Example: Find |­3 + 4i|
Day 1 Trig form of complex numbers
December 05, 2014
imaginary
(a, b)
Example: Express 2 + 2i in trig form
real
Try These: Represent the complex number graphically, and find the trigonometric form of the number.
1.) 4 ­ 4√3 i
Find the standard form of the number.
3.) 3 (cos 300 + i sin 300 )
2
Example: Express 5(cos 135 + i sin 135 ) in standard form
2.) 4i