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z1 = x + iy

z2 = x - iy

(Complex conjugate)

Find:

Im (1/z1)

This is what I have tried to do:

(1) z1*z2 = x^2 + y^2

(2) z2 / (x^2 + y^2) = 1 / z1

The answer is:

-y / (x^2 + y^2) = I am (1 / z1)

So my question is:

Can I change z2 to I am (z2) and z1 to I am (z1) in equation (2)?

z2 = x - iy

(Complex conjugate)

Find:

Im (1/z1)

This is what I have tried to do:

(1) z1*z2 = x^2 + y^2

(2) z2 / (x^2 + y^2) = 1 / z1

The answer is:

-y / (x^2 + y^2) = I am (1 / z1)

So my question is:

Can I change z2 to I am (z2) and z1 to I am (z1) in equation (2)?

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