# Math Help - Multiplication of complex numbers

1. ## Multiplication of complex numbers

If z = 3 + 4i and w = 1 - 2i, calculate:

(z - w)²

Please show any working out. Thanks.

2. Originally Posted by Joker37
If z = 3 + 4i and w = 1 - 2i, calculate:

(z - w)²

Please show any working out. Thanks.
$z - w = (3 + 4i) - (1 - 2i) = 2 + 6i
$

now calculate $(2 + 6i)^2$

3. Hello, Joker37!

This is straight-forward algebra.
$\text{If }\,z \,=\, 3 + 4i\text{ and }w \,=\, 1 - 2i,\text{ calculate: }\:(z - w)^2$
$z - w \:=\:(3+4i) - (1-2i) \;=\;3 + 4i - 1 + 2i \;=\;2 + 6i$
$(z\:-\:w)^2 \;=\;(2\:+\:6i)(2\:+\:6i) \;=\;4\:+\:12i\:+\:12i\:+\:36i^2 \;=\;4\:+\:24i\:-\:36$ . $=\;-32\:+\:24i$