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

Aug 12, 2016

$- 8 i$

#### Explanation:

Expand each bracket using, say ,the FOIL method.

$\Rightarrow {\left(1 - 2 i\right)}^{2} - {\left(1 + 2 i\right)}^{2}$

$= 1 - 4 i + 4 {i}^{2} - \left(1 + 4 i + 4 {i}^{2}\right)$

$= 1 - 4 i + 4 {i}^{2} - 1 - 4 i - 4 {i}^{2} = - 8 i$

Alternatively, note that the expression is a $\textcolor{b l u e}{\text{difference of squares}}$ and factorises as follows.

$\left[\left(1 - 2 i\right) - \left(1 + 2 i\right)\right] \left[\left(1 - 2 i\right) + \left(1 + 2 i\right)\right]$

$= \left(- 4 i\right) \left(2\right) = - 8 i$