Question

18 - 24i write in trigonometric form

Answer 1

$\boxed{18-24i=30(cos(5.36)+isin(5.36))}$

Explanation:

Unlike 0, we can write any complex number in the trigonometric form:

$z=r(cos\alpha+isin\alpha)$

We have the complex number:

$18-24i$

So $r$ can be found as:

$r=\sqrt{x^2+y^2} \\ \\ \\ Where: \\ \\ x=18 \\ \\ y=-24 \\ \\ r=\sqrt{18^2+(-24)^2} \\ \\ r=\sqrt{324+576} \\ \\ r=\sqrt{900} \\ \\ r=30$

Now for α:

$\alpha=arctan(\frac{y}{x}) \\ \\ Since \ the \ complex \ number \ lies \ on \ the \ fourth \ quadrant: \\ \\ \alpha=arctan(\frac{-24}{18})=-53.13^{\circ}  \ or \ 360-53.13=306.87^{\circ}$

Finally:

$Convert \ into \ radian: \\ \\ 360^{\circ}\times \frac{\pi}{180}=5.36rad \\ \\ \\ Hence: \\ \\ \boxed{18-24i=30(cos(5.36)+isin(5.36))}$

Learn more:

Complex conjugate: https://brainly.com/question/2137496

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