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 i2 term is then replaced with -1.
If h = 3 + 4i and j = 1 + 6i
h.j = (3 + 4i)(1 + 6i)
= 3 + 18i + 4i + 24i2
= 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.
If s = 2 + 5i and t = 3 + 4i
Note that the answer to this type of problem is left in rectangular form, a + bi.