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: [tex]r = \sqrt{x^2 +y^2} = \sqrt{12^2 + 16^2} = \sqrt{400} = 20[/tex] Finally, calculate theta: [tex]\theta = \tan^{-1}(\frac{y}{x}) = \tan^{-1} (\frac{16}{-12}) = 126.87[/tex] 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: [tex]-12 + 16i = 20(\cos 126.87 + i \sin 126.87)[/tex]
