Multiplication of complex numbers

• December 27th 2008, 11:23 AM
Joker37
Multiplication of complex numbers
If z = 3 + 4i and w = 1 - 2i, calculate:

(z - w)²

Please show any working out. Thanks.
• December 27th 2008, 11:33 AM
skeeter
Quote:

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 $(2 + 6i)^2$
• December 27th 2008, 11:44 AM
Soroban
Hello, Joker37!

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