Complex numbers can be multiplied together and divided just like other types of numbers.

### Multiplying Complex Numbers

The multiplication of complex numbers is similar to expanding brackets in a quadratic. The i^{2} term is then replaced with -1.

**Example**

If h = 3 + 4i and j = 1 + 6i

h.j = (3 + 4i)(1 + 6i)

= 3 + 18i + 4i + 24i

^{2}= 3 + 22i + 24(-1)

= 3 + 22i – 24

= -21 + 22i

### Dividing Complex Numbers

The division of complex numbers is similar to the rationalisation of a denominator in a fraction containing surds.

The algebraic fraction formed by the division is multiplied by a fraction containing the conjugate of the denominator.

**Example**

If s = 2 + 5i and t = 3 + 4i

Note that the answer to this type of problem is left in **rectangular **form, a + bi.