# 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.

### Relevant Questions Determine the absolute value of the complex number z=2-3i Determine the absolute value of each of the following complex numbers:
a. z = 3 + 4i
b. z = -1 - 2i. Determine the absolute value of the complex number $$\displaystyle{2}-{3}{i}$$. Determine the absolute value of each of the following complex numbers:
a. z = 5 + 12i
b. 2 - 3i. Determine the location and value of the absolute extreme value of f on the given interval, if they exist.
$$\displaystyle{f{{\left({x}\right)}}}={x}\ {\ln{{\frac{{{x}}}{{{5}}}}}}\ {o}{n}\ {\left[{0.1},{5}\right]}$$ Find the absolute value of $$\displaystyle{z}={3}+{2}{i}$$ What is the absolute value of $$\displaystyle-{7}{\frac{{{3}}}{{{4}}}}$$. The absolute value of -6 is equal to the distance on a number line between.
1)-6 an 6
2)-6 and 1
3)0 and 6
4)1 and -6 a)$$\displaystyle{\left|{-{7}}\right|}$$
b)$$\displaystyle{\left|{-{2}}\right|}$$
c)$$\displaystyle{\left|{{6}}\right|}$$
d)$$\displaystyle{\left|{{0}}\right|}$$ 