Blog: `-6 + 8i` Plot the complex number and find its absolute value.

Saturday, April 16, 2016

$\displaystyle-{6}+{8}{i}$ Plot the complex number and find its 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:

$\displaystyle{a}=-{6},{b}={8}$

$\displaystyle{\left|{z}\right|}=\sqrt{{{{\left(-{6}\right)}}^{{2}}+{{8}}^{{2}}}}$

$\displaystyle{\left|{z}\right|}=\sqrt{{{36}+{64}}}$

$\displaystyle{\left|{z}\right|}=\sqrt{{100}}$

$\displaystyle{\left|{z}\right|}={10}$

Hence, the distance of the complex number $\displaystyle{z}=-{6}+{8}{i}$ from the origin is given by its absolute value $\displaystyle{\left|{z}\right|}={10}$ .

In the Argand diagram, the complex number $\displaystyle{z}=-{6}+{8}{i}$ is the point $\displaystyle{\left(-{6},{8}\right)}$ or the vector from the origin to the point $\displaystyle{\left(-{6},{8}\right)}$ .

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Saturday, April 16, 2016

$\displaystyle-{6}+{8}{i}$ Plot the complex number and find its absolute value.

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