Unit 5 - Objective 4 – Polar Form of a Complex Number
Quick Review
The rectangular form is not the only way to represent complex numbers.
The angle 
that the vector makes with the positive real axis is called the argument of the complex number. The length r is the called the absolute value of the complex number. The absolute value is a real number that is never negative. Using the Pythagorean Theorem, the length of r gives 
.
Given x + yj is a vector in the complex plane then r=
is
the magnitude of the vector. Since 
and 
then x + yj = 
The expansion 
is often abbreviated as 
(r at angle )
So is called the polar or trigonometric form of a complex number.
Examples
- Represent (5 -12j) graphically and convert it to polar form.
So 
Since we usually use the smallest positive value for we would use 
=360 degrees - 67.4 degrees. So 
- Represent –5 + 7.5j graphically and convert it to polar form
