The Basics

Solving complex numbers:

Complex number is a number that can be expressed in the form z= r+bi. (r is the real part and b is the imaginary part), the real part and the imaginary part of a complex number cannot be combined. Solving complex numbers with the use of common operators are easy. 

Complex number operations:

Sample problem

z1=x1+j(y1)
z2=x2+j(y2)

Addition:

Add the real part and the imaginary part.
          z1+z2= (x1+x2) + j(y1+y2)

Subtraction:
Subtract the real part and the imaginary part.
          z1-z2= (x1-x2) + j(y1-y2)   

Multiplication:
Multiply the real part then add the angles. (This method can be only used when the complex number is converted to Polar form.)
          x1*x2∟ᴓ1+ ᴓ2

Division:
Divide the real part then subtract the angles. (This method can be only used when the complex number is converted to Polar form.)
          x1/x2∟ᴓ1- ᴓ2