complex Numbers

Submitted by alpha on Sun, 04/03/2011 - 05:01.

If $log _{\frac{1}{2}}\frac{[|z|^2 +2|z|+4}{[2|z|^2+1]]}<0$ , then the region traced by z is
i) $|z|<3$
ii) $1<|z|<3$
iii) $|z|>1$
iv) $|z|<2$

Please show the working. I'm more interested in knowing the procedure.

Thanks in advance.

$\frac{|z|^2 +2|z|+4}{2|z|^2+1}>1$

$|z|<3$