Question

How do you simplify $\left(x-2+3i\right)\left(x-2-3i\right)$?

Answer 1

Simplify the expression:

Given expression is $\left(x-2+3i\right)\left(x-2-3i\right)$.

Rewrite the expression as follows,

$\left(x-2+3i\right)\left(x-2-3i\right)=\left(\left(x-2\right)+3i\right)\left(\left(x-2\right)-3i\right)$

Apply $\left(a+bi\right)\left(a-bi\right)=a^2+b^2$

So,

$\begin{array}{rcl}\left(\left(x-2\right)+3i\right)\left(\left(x-2\right)-3i\right)& =& {\left(x-2\right)}^2+3^2\\ & =& x^2-4x+4+9\\ & =& x^2-4x+13\end{array}$

Hence, $\left(x-2+3i\right)\left(x-2-3i\right)\mathbf{}\mathbf{\text{is equal to}}\mathbf{}{\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{4}\mathit{x}\mathbf{+}\mathbf{13}$.