## Algebra 2 Common Core

$|2-2i|=2\sqrt{2}$
The plot of the given complex number, $2-2i ,$ is shown below. The absolute value of the complex number $a+bi,$ written as $|a+bi|,$ is given by $\sqrt{a^2+b^2}.$ Therefore, the absolute value of the given complex number is \begin{align*} & \sqrt{(2)^2+(-2)^2} \\&= \sqrt{4+4} \\&= \sqrt{8} \\&= \sqrt{4\cdot2} \\&= 2\sqrt{2} .\end{align*} Hence, $|2-2i|=2\sqrt{2} .$