Blog: `-8 + 3i` Plot the complex number and find its absolute value.

Thursday, May 10, 2012

$\displaystyle-{8}+{3}{i}$ 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:

$\displaystyle{a}=-{8},{b}={3}$

$\displaystyle{\left|{z}\right|}=\sqrt{{{{\left(-{8}\right)}}^{{2}}+{{3}}^{{2}}}}$

$\displaystyle{\left|{z}\right|}=\sqrt{{{64}+{9}}}$

$\displaystyle{\left|{z}\right|}=\sqrt{{73}}$

Hence, the distance of the complex number $\displaystyle{z}=-{8}+{3}{i}$ from the origin is given by its absolute value $\displaystyle{\left|{z}\right|}=\sqrt{{73}}$ .

In the Argand diagram, the complex number $\displaystyle{z}=-{8}+{3}{i}$ is the point (-8,3) or the vector from the origin to the point (-8,3).

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Thursday, May 10, 2012

$\displaystyle-{8}+{3}{i}$ Plot the complex number and find its absolute value.

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