Write -3+4i in the form r(cosx+isinx)

is a complex number that satisfies



The last equation immediately tells you that .

So you have



Dividing the second equation by the first, you end up with



Because the argument's cosine is negative and its sine is positive, you know that . This is important to know because it's only the case that whenever . The inverse doesn't exist otherwise.

However, you can restrict the domain of the tangent function so that an inverse can be defined. By shifting the argument of tangent by , we have



All this to say



So, .