#### Edema

Write in u and v
F(z) = e^z + 2z

And
F{z} = 1/(z^2 + 2z + 1 )

F{z} = z^2 + 1 / z^2 - 1

#### DarnItJimImAnEngineer

What are u and v?

topsquark

#### DarnItJimImAnEngineer

The real and imaginary parts of what? ...of F?
Is z a complex number?

topsquark

#### Edema

Yes of course z is a complex number while yes ooooooouuuu haaaaa It's F

#### DarnItJimImAnEngineer

OK, so let's write $z = x + iy$, $F = u + iv$.
$F(x+iy) = e^{(x+iy)} + 2(x+iy) = e^x e^{iy} + 2x + 2iy$
Remember Euler's identity, $e^{iy} = \cos(y) + i\sin(y)$.

Multiply out, then combine all the real terms (u) and all the imaginary terms (v).

The second and third functions are comparatively easier. Just remember to bring all of the $i$ terms to the numerator when you simplify.