Express the given function in terms of its real and imaginary parts. Perform this decomposition:
1) In rectangular coordinates z = x + iy, and
2) In polar coordinates z = re^(it)
\[
\displaylines{f\left(z\right)=z+\frac{1}{z}\\ 1)f\left(x,y\right)=u\left(x,y\right)+iv\left(x,y\right)\\ 2)f\left(r,\theta\right)=u\left(r,\theta\right)+iv\left(r,\theta\right)}
\]