Mathematics: Write the complex number -12+16i in trigonometric form r(cos theta+i sin theta), with theta in the interval

Write the complex number -12+16i in trigonometric

Ответ:

brendaslater49p6ttxt

01.01.2022

First identify which quadrant we are in:
x = real = -12
y = imaginary = 16
(-12,16) is in 2nd quadrant, this means theta is between 90 and 180.

Next calculate "r", which is distance from (-12,16) to origin:
$r = \sqrt{x^2 +y^2} = \sqrt{12^2 + 16^2} = \sqrt{400} = 20$
Finally, calculate theta:
$\theta = \tan^{-1}(\frac{y}{x}) = \tan^{-1} (\frac{16}{-12}) = 126.87$
Note: when you put this in your calculator it will give you -53.13 (4th quadrant)
Just add 180 so that angle is in correct quadrant.
Final
$-12 + 16i = 20(\cos 126.87 + i \sin 126.87)$

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Ответ:

jobmoon

31.12.2020

Mathematics

dude i try to but people keep reporting me and calling me a karen so i stopped

Step-by-step explanation:

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Write the complex number -12+16i in trigonometric form r(cos theta+i sin theta), with theta in the interval

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