## Algebra 2 (1st Edition)

$|7+7i|=7\sqrt{2}$
The absolute value of a complex number $z=a+bi,$ denoted $|z|,$ is a nonnegative real number defined as $|z|=\sqrt{a^{2}+b^{2}}$. $|z|=|7+7i|$ $=\sqrt{a^{2}+b^{2}}\qquad$ ...substitute $7$ for $a$ and $7$ for $b$ $=\sqrt{7^{2}+7^{2}}\qquad$ ...simplify. $=\sqrt{49+49}$ $=\sqrt{98}\qquad$ ...rewrite as $\sqrt{49\cdot 2}=7\sqrt{2}$ $=7\sqrt{2}$