Prove that $z_n\rightarrow z=r(cos(A)+isin(A))$ iff $r_n\rightarrow r$ and $A_n\rightarrow A$

Prove that $z_n\rightarrow z=r(cos(A)+isin(A))$ iff $r_n\rightarrow r$ and
$A_n\rightarrow A$

$z_n=r_n(cos(A_n)+isin(A_n))$ and $z=r(cos(A)+isin(A))$
Prove that $z_n\rightarrow z=r(cos(A)+isin(A))$ as $n\rightarrow \infty$
if and only if $r_n\rightarrow r$ and $A_n\rightarrow A$ as $n\rightarrow
\infty$
This is a question I just thought of myself. I was trying to use
$\epsilon$ and $\delta$ definition of the limit but was hard to do.