Answer
$|7+7i|=7\sqrt{2}$
Work Step by Step
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 $\sqrt{49\cdot 2}=7\sqrt{2}$
$=7\sqrt{2}$
