Operations on complex numbers in polar form
Operations on complex numbers in polar form
Let's find out how to perform some basic operations on complex numbers in polar form! We will briefly introduce the notion of the exponential form of a complex number, then we will focus on multiplication and division on complex numbers in polar form.
Basic concepts:
 Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$
 Exponents: Division rule ${a^x \over a^y}=a^{(xy)}$
Related concepts:
 Imaginary zeros of polynomials
Lessons
Notes:
Note:
Polar form real part$a=z\cos \theta$
imaginary part$b=z\sin \theta$
$z=z(\cos \theta+i\sin \theta)$
When …
Multiplying: multiply the absolute values, and add the angles
Dividing: divide the absolute values, and subtract the angles
Exponential form$z=ze^{i \theta}$

1.
Multiplying complex numbers in polar form

2.
Dividing complex numbers in polar form