1. The problem statement, all variables and given/known data I'm asked to calculate Green's function's real and imaginary parts. The expression for the given Green's function is: g00=[1-(1-4t2(z-E0)-2)1/2]/2t2(z-E0)-1 (1) Where, z is the complex variable: z= E+iO+ (2) 2. Relevant equations Complex number definition: Z = x + iy, where x is the real part and iy - imaginary. 3. 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.