Notes: `5 - 12i` Find complex number absolute value.

Sunday, 7 May 2017

$\displaystyle{5}-{12}{i}$ Find complex number absolute value.

The absolute value of a complex number $\displaystyle{z}={a}+{b}\cdot{i}$ is $\displaystyle{\left|{z}\right|}=\sqrt{{{{a}}^{{2}}+{{b}}^{{2}}}}.$ According to this formula, you need to determine a and b, such that:

$\displaystyle{a}={5},{b}=-{12}$

$\displaystyle{\left|{z}\right|}=\sqrt{{{{5}}^{{2}}+{{\left(-{12}\right)}}^{{2}}}}$

$\displaystyle{\left|{z}\right|}=\sqrt{{{25}+{144}}}$

$\displaystyle{\left|{z}\right|}=\sqrt{{169}}$

$\displaystyle{\left|{z}\right|}={13}$

Hence, the distance of the complex number $\displaystyle{z}={5}-{12}{i}$ from the origin is given by its absolute...

$\displaystyle{a}={5},{b}=-{12}$

$\displaystyle{\left|{z}\right|}=\sqrt{{{{5}}^{{2}}+{{\left(-{12}\right)}}^{{2}}}}$

$\displaystyle{\left|{z}\right|}=\sqrt{{{25}+{144}}}$

$\displaystyle{\left|{z}\right|}=\sqrt{{169}}$

$\displaystyle{\left|{z}\right|}={13}$

Hence, the distance of the complex number $\displaystyle{z}={5}-{12}{i}$ from the origin is given by its absolute value $\displaystyle{\left|{z}\right|}={13}$ .