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.
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).
(a + ib) + (c + id) = (a + c) + i(b + d)
(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.
(a + ib)(c + id) = ac + iad + ibc + i2bd
= (ac − bd) + i(ad + bc)