Compute $|z|$ , $z = \frac{(2+i)^7(1-2i)^3}{(1+2i)^8}$ Compute $|z|$ , $z = \frac{(2+i)^7(1-2i)^3}{(1+2i)^8}$,
if $z = a+ib$ then,
I tried to do that with $|z| = (a+ib)(a-ib)$
then i multipled it $z$ with $z^-$ and then I got stuck. answer is $|z| = 5$

Hint. One may write
$$
|z|^2=z\cdot \bar z=\frac{|2+i|^{14}|1-2i|^6}{|1+2i|^{16}}=\frac{(2^2+1^2)^7(1^2+2^2)^3}{(1^2+2^2)^8}.
$$
