Answer
$|z|=\sqrt{29}$
see graph below
.
Work Step by Step
See p. 602, Graphing Complex Numbers
The complex plane is determined by the real axis and the imaginary axis.
To graph the complex number a + bi, we plot the ordered pair of numbers (a,b) in this plane
See p. 603,
The modulus (or absolute value) of the complex number $z=a+bi$ is
$|z|=\sqrt{a^{2}+b^{2}}$
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$z=5+2i$
$(a,b)=(5,2)$
Plot $(5,2)$ in the complex plane (see image).
$|z|=\sqrt{5^{2}+2^{2}}=\sqrt{29}$