Blog: `12i` Write the trigonometric form of the number.

Saturday, January 30, 2016

$\displaystyle{12}{i}$ Write the trigonometric form of the number.

The trigonometric form of a nonzero complex number is

$\displaystyle{r}\cdot{\left({\cos{\theta}}+{i}\cdot{\sin{\theta}}\right)},$

where $\displaystyle{r}\gt{0}$ is the absolute value of a number and $\displaystyle\theta\in{\left[{0},{2}\pi\right)}$ is the argument.

For this number the absolute value is obviously 12. Also this number lies on the positive half of the y-axis, therefore $\displaystyle\theta=\frac{\pi}{{2}}.$

The answer: $\displaystyle{12}{i}={12}{\left({\cos{{\left(\frac{\pi}{{2}}\right)}}}+{i}\cdot{\sin{{\left(\frac{\pi}{{2}}\right)}}}\right)}.$

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Saturday, January 30, 2016

$\displaystyle{12}{i}$ Write the trigonometric form of the number.

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