Complex number is a number made up of real numbers and imaginary numbers. Complex number,denoted as z, is represented in the form of the following expression: z = a + bi, where a is the real number and b is the imaginary part of the complex number. Unit imaginary number "i" is equal to square root of -1, i.e  $i = \sqrt{-1}$
Complex number can be represented in an ordered pair (a,b) and plotted in a plan known as complex plane.
                                           Complex Number
Addition and Subtraction Operation:

To add or subtract two complex numbers,the rule is to add or subtract real and imaginary parts separately.
       $(a + bi) + (c + di) = (a + c) + i(b + d)$
       $(a + bi) - (c + di) = (a - c) + i(b - d)$
      
Multiplication Operation:

To multiply two complex numbers,multiply each first complex number with second complex number.      
        $(a + bi)(c + di) = ac + adi + bci + bdi^{2}$
                    as $i^{2} = -1$
        $(a + bi)(c + di) = ac + adi + bci - bd$
        $(a + bi)(c + di) = (ac - bd) + i(ad + bc)$

Division Operation:

To divide two complex numbers, we need to multiply both denominator and numerator by conjugate of denominator.
         $\frac{(a + bi)}{(c + di)} = \frac{(a + bi)}{(c + di)}\times \frac{(c - di)}{(c - di)}$
         $\frac{(a + bi)}{(c + di)} = \left (  \frac{ac + bd}{c^{2} + d^{2}}\right )+ i\left ( \frac{bc - ad}{c^{2} + d^{2}} \right )$