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

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:

Finally, calculate theta:

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

Answers4.) -1/205.) -1/406.) -55/127.) -3/4