solving complex equation in matlab

I was just wondering how to solve an equation in attachment for 'n' which involves real and imaginary part.

Thanks

Answer 1

[Roger Stafford]

 n = 1/k0/d*atan2(sqrt(1-X^2),X)

and

 n = 1/k0/d*atan2(-sqrt(1-X^2),X)

All other solutions differ from these by integral multiples of 2*pi/k0/d.

Answer 2

[Walter Roberson]

Use a small bit of algebra. Take the ln of both sides and rearrange terms.

n = -i * ln(X +/- i*sqrt(1-X^2)) / (K0 * d)