(1) The complex plane defines complex numbers as points (a, b) where a is the real component and b is the imaginary component, plotted on an x-y plane. (2) Absolute value of a complex number z = a + bi is the distance of z from the origin, found using the Pythagorean theorem. (3) Complex numbers can also be written in polar form as r(cosθ + i sinθ) where r is the absolute value and θ is the argument.

1. Precalculus
9-6 Complex Plane and Polar Form of Complex Numbers
Plotting Complex Numbers
Define the complex plane:
Plot (a) z = 3 + 2ι
(b) z = 4 ι
Absolute Value means ____________________________________________________.
Use Pythagorean Theorem to find absolute value of a complex number:
Find the absolute values of the examples above.
Complex Numbers as Polar Coordinates
What is r? __________________________________________
• This is also called the ____________________ of the complex number.
θ is called the _________________________ of the complex number.
Complex numbers can be written in polar form by substituting a = ρχοσθ and b = ρσ θ .
ιν
Polar form of a + βι is _______________________

2. EX1: Solve the equation for x and y, where x and y are real numbers.
2x + ψ+ 3ι = 9 ξι − ψι
EX2: Express the complex number in polar form.
−3 + 4i
1+ ι 3
HW p. 590 (16 – 34 even)