Algebraic Operations of Complex Numbers

Equality of Complex Numbers

Two complex numbers a + ib and c + id are equal if and only if a = c and b = d. The corresponding real parts are equal and the corresponding imaginary parts are equal.

Negative of Complex Number

If z = a + ib is a complex number, then the negative of z is denoted by −z and it is defined as −z = −a + i(−b).

Basic Algebraic Operations

Addition

(a + ib) + (c + id) = (a + c) + i(b + d)

Subtraction

(a + ib) − (c + id) = (a − c)+ i(b − d)

To perform the operations with complex numbers, you can proceed as in the algebra of real numbers replacing i² by −1 whenever it occurs.

Multiplication

(a + ib)(c + id) = ac + iad + ibc + i²bd

= (ac − bd) + i(ad + bc)