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## Homework Statement

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

The expression for the given Green's function is:

g

_{00}=[1-(1-4t

^{2}(z-E

_{0})

^{-2})

^{1/2}]/2t

^{2}(z-E

_{0})-

^{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 g

_{00}in the form: g

_{00}= x+iy

First I simplified the (1) by multiplying the denominator and numerator by (z-E

_{0}).

The result is g

_{00}= 1/2t

^{2}[(z-E

_{0})-(1-4t

^{2})]

^{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.