Complex Logarithm: Solving tan-1[(2sqrt(3) - 3i)/7]

[metgt4]

Homework Statement

If

tan^-1z = (1/2i)ln[(1+iz)/(1-iz)]

then find

tan^-1[(2sqrt(3) - 3i)/7]

The Attempt at a Solution

I haven't gotten very far, but this is what I have so far:

tan^-1[(2sqrt(3) - 3i)/7]

= (1/2i)ln[(i2sqrt(3) + 10)/(i2sqrt(3) + 4)]

Where do you go from there? I'm not completely familiar with the rules of complex logarithms. Can you split it into real and imaginary parts?

 

[Dick]

You should check what you already have. I think you've already got a sign wrong. But you want write the expression inside the log in the form a+bi with a and b real, so you can find it's magnitude and angle. You know how to do that with a ratio using complex conjugates, right?