For each part below, calculate all quantities that are not given from the following list:

F $($z$),\backslash$phi $,\backslash$psi $,$ w$($z$),$ ~v

Note that F $($z$)$ is the complex potential, $\backslash$phi is the velocity potential, $\backslash$psi is the stream function, w$($z$)$

is the complex velocity, and ~v is the real velocity. If a quantity does not exist, state why not.

i$)$ F $=(1/3)$iz$3$

ii$)\backslash$psi $=$ ex cos$($y$)$

iii$)\backslash$phi $=$ ln $($x$2+$ y$2)$

iv$)$ w $=$ z $+1/$z

v$)$ ~v $=$ x$$i $+$ y$$j