Blog: `4 - 6i` Plot the complex number and find its absolute value.

Friday, June 26, 2015

$\displaystyle{4}-{6}{i}$ Plot the complex number and find its absolute value.

You need to find the absolute value of the complex number, using the formula $\displaystyle{\left|{z}\right|}=\sqrt{{{{a}}^{{2}}+{{b}}^{{2}}}}$ , hence, you need to determine a and b.

$\displaystyle{a}={4},{b}=-{6}.$

Replacing 4 for a and -6 for b in formula of absolute value, yields:

$\displaystyle{\left|{z}\right|}=\sqrt{{{{4}}^{{2}}+{{\left(-{6}\right)}}^{{2}}}}$

$\displaystyle{\left|{z}\right|}=\sqrt{{{16}+{36}}}$

$\displaystyle{\left|{z}\right|}=\sqrt{{52}}\Rightarrow{\left|{z}\right|}={2}\sqrt{{13}}$

Hence, the distance of the complex number $\displaystyle{z}={4}-{6}{i}$ from the origin is given by the aboslute value $\displaystyle{\left|{z}\right|}={2}\sqrt{{13}}$ .

The complex number $\displaystyle{z}={4}-{6}{i}$ is displayed as the point (4,-6) in a coordinate plane, or as a vector from the origin to the point (4,-6).

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Friday, June 26, 2015

$\displaystyle{4}-{6}{i}$ Plot the complex number and find its absolute value.

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