$\text{ Let }z\in C\text{ , if }A=\left\{z:\arg \left(z\right)=\frac{\pi }{4}\right\}\text{ and }B=\left\{z:\arg (z-3-3i)=\frac{2\pi }{3}\right\}\text{ then }$$n(A\cap B)\text{ is equal to }$

$\mathrm{Arg}\left(z\right)=\frac{\pi }{4}$

$\begin{array}{l}\Rightarrow Ta{n}^{-1}\left(\frac{y}{x}\right)=\frac{\pi }{4}\\ \Rightarrow y=x(x>0,y>0)\end{array}$

$\begin{array}{l}\arg (z-3-3i)=\frac{2\pi }{\begin{array}{l}3\\ \end{array}}\\ Ta{n}^{-1}\left(\frac{y-3}{x-3}\right)=2\pi /3\\ y-3=-\sqrt{3}\left(x-3\right)\left(y-3>0,x-3<0\right)\end{array}$

We can observe that 

$3+3\mathrm{i}\in A\text{ but }\notin B$

$\therefore n\left(A\cap B\right)=0$