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

Circuits 2

In circuits 1 we started studying the basic concepts of electric circuit and its fundamentals. Circuits with direct current are also analyzed. But now that we are in circuits 2, we will start dealing with complex numbers and start analyzing AC circuits.