I'm asked to calculate Green's function's real and imaginary parts.
The expression for the given Green's function is:
Where, z is the complex variable: z= E+iO+ (2)
Complex number definition: Z = x + iy, where x is the real part and iy - imaginary.
The Attempt at a Solution
To separate real and imaginary parts I tried to express g00 in the form: g00= x+iy
First I simplified the (1) by multiplying the denominator and numerator by (z-E0).
The result is g00= 1/2t2[(z-E0)-(1-4t2)]1/2.
Then I'm stuck. I don't know how to remove the square root to divide real and imaginary parts. I'm not even sure if it is the pure math problem or if I have to take into consideration anything else.
I would appreciate any help.