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Write -3 + 5i in trigonometric form r( cosx + I sinx)

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Answer to a math question Write -3 + 5i in trigonometric form r( cosx + I sinx)

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Rasheed
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105 Answers
r = \sqrt{(-3)^2 + 5^2} = \sqrt{9 + 25} = \sqrt{34}

\theta = \tan^{-1} \left( \frac{5}{-3} \right) + \pi = \tan^{-1} \left( \frac{-5}{3} \right) + \pi = \tan^{-1} \left( -\frac{5}{3} \right) + \pi

Thus, the trigonometric form is:

\sqrt{34} \left( \cos \left( \tan^{-1} \left( -\frac{5}{3} \right) + \pi \right) + i \sin \left( \tan^{-1} \left( -\frac{5}{3} \right) + \pi \right) \right)

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