$f(z)=1/2^z$
$z=x+iy$
$f(z)=1/2^(x+iy)=1/(2^x*2^(iy))=1/(2^x*e^(iyln2))=1/(2^x*(cosyln2+isenyln2))=$
$=1/(2^x*(cosyln2+isenyln2))*(cosyln2-isenyln2)/(cosyln2-isenyln2)=$
$=(cosyln2-isenyln2)/(2^x((cosyln2)^2+(senyln2)^2))=$
$=(cosyln2)/(2^x((cosyln2)^2+(senyln2)^2))-(senyln2)/(2^x((cosyln2)^2+(senyln2)^2))*i$
$f(z)=|z|=sqrt (x^2+y^2)$
$r=sqrt(((cosyln2)/(2^x((cosyln2)^2+(senyln2)^2)))^2+(-(senyln2)/(2^x((cosyln2)^2+(senyln2)^2)))^2$