Question

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

Answer 1

`-8i`

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`