# Determine the absolute value of the complex number z = 5 + 12i

Determine the absolute value of the complex number $z=5+12i$

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Step 1
We have to find absolute value of complex number:
$z=5+12i$
We know that if we have complex number $z=x+iy$ then its absolute value will be,
$|z|=\sqrt{{x}^{2}+{y}^{2}}$
Comparing the complex number $z=5+12i$ with $z=x+iy,$ we get
$x=5$
$y=12$
Where,
x is real part of complex number
and y is the imaginary part of the complex number.
Step 2
Applying above formula for the given complex number,
$|z|=\sqrt{{x}^{2}+{y}^{2}}$
$=\sqrt{{5}^{2}+{12}^{2}}$
$=\sqrt{25+144}$
$=\sqrt{169}$
$=13$
Hence, absolute value of complex number is 13.

Jeffrey Jordon