# How do you perform the operation and write the result in standard form given #(1-2i)^2-(1+2i)^2#?

##### 1 Answer

Aug 12, 2016

#### Explanation:

Expand each bracket using, say ,the FOIL method.

#rArr(1-2i)^2-(1+2i)^2#

#=1-4i+4i^2-(1+4i+4i^2)#

#=1-4i+4i^2-1-4i-4i^2=-8i# Alternatively, note that the expression is a

#color(blue)"difference of squares"# and factorises as follows.

#[(1-2i)-(1+2i)][(1-2i)+(1+2i)]#

#=(-4i)(2)=-8i#