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

Question
Piecewise-Defined Functions
Determine the absolute value of the complex number z = 5 + 12i

2021-02-04
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,
$$\displaystyle{\left|{{z}}\right|}=\sqrt{{{x}^{{2}}+{y}^{{2}}}}$$
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,
$$\displaystyle{\left|{{z}}\right|}=\sqrt{{{x}^{{2}}+{y}^{{2}}}}$$
$$\displaystyle=\sqrt{{{5}^{{2}}+{12}^{{2}}}}$$
$$\displaystyle=\sqrt{{{25}+{144}}}$$
$$\displaystyle=\sqrt{{{169}}}$$
=13
Hence, absolute value of complex number is 13.

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