Question

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

Answer 1

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 = √(x^2 +y^2) = √(12^2 + 16^2) = √(400) = 20`
Finally, calculate theta:

`\theta = \tan^(-1)((y)/(x)) = \tan^(-1) ((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 Answer:

`-12 + 16i = 20(\cos 126.87 + i \sin 126.87)`