Find the real and imaginary parts of the following functions as functions of $\displaystyle x$ and $\displaystyle y$.
(i) $\displaystyle z^3$
(iii) $\displaystyle (z+z^{-1}) \ (z\ne 0)$
(vi) $\displaystyle {1\over 1-z} \ (z\ne 1)$
Find the real and imaginary parts of the following functions as functions of $\displaystyle x$ and $\displaystyle y$.
(i) $\displaystyle z^3$
(iii) $\displaystyle (z+z^{-1}) \ (z\ne 0)$
(vi) $\displaystyle {1\over 1-z} \ (z\ne 1)$
1° $\displaystyle (x+iy)^3 $ solve and group numbers with "i" and without it so those with "i" will be imaginary ones ...
2° $\displaystyle \displaystyle (x+iy) + \frac {1}{x+iy} $ add those than multiply with $\displaystyle \displaystyle \frac {x-iy}{x-iy} $ and than group Re and Im
6°$\displaystyle \displaystyle \frac {1}{1-x - iy } $ this one multiply with $\displaystyle \displaystyle \frac {1-x+iy}{1-x+iy}$ than do same thing