A) \[\frac{|z|}{2}\]
B) \[|z|\]
C) \[2|z|\]
D) None of these
Correct Answer: A
Solution :
\[\operatorname{z}=1+2i\,\,\Rightarrow \,\,\left| z \right|=\,\,\sqrt{1+4}=\sqrt{5}\] \[\therefore \,\,\,f(z)=\frac{7-z}{1-{{z}^{2}}}=\frac{7-1-2i}{1-{{(1+2i)}^{2}}}\] \[=\,\,\frac{6-2i}{1-(1-4+4i)}=\frac{6-2i}{4-4i}=\frac{3-i}{2-2i}\] \[\Rightarrow \,\,\,\left| f\,(z) \right|=\left| \frac{3-i}{2-2i} \right|=\frac{\left| 3-i \right|}{\left| 2-2\,i \right|}\] \[=\,\,\frac{\sqrt{9+1}}{\sqrt{4+4}}=\frac{\sqrt{5}}{2}=\frac{\left| z \right|}{2}\]
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