# Green's Function Homework: Real & Imaginary Parts

• Mancho

## Homework Statement

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)

## Homework Equations

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.

Welcome to PF!

I'm asked to calculate Green's function's real and imaginary parts.

I don't know how to remove the square root to divide real and imaginary parts.

Hi Mancho! Welcome to PF! Hint: the square-root of re is (√r)eiθ/2, and so its real and imaginary parts are (√r)cos(θ/2) and (√r)sin(θ/2) Thanks a lot tiny-tim!

I guessed from your hint I had to use polar coordinates and it worked great! I got what I was supposed to. Maybe I will upload the solution later when I have time.

Thanks again! :)