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.

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.