Question

Pls solve this also (°-°)​

Answer 1

$\large\rm{f(z) = \frac{7-z}{1-z^{2}}}$

$\large\rm { = \frac{7-(1+2i)}{1-(1+2i)^{2}}}$

$\large\rm { = \frac{6-2i}{1-1+4-4i}}$

$\large\rm { = \frac{6-2i}{4-2i}}$

$\large\rm { = \frac{6-2i}{4-2i} \times \frac{4+4i}{4+4i}}$

$\large\rm { = 1 + \frac{1}{2} i}$

since $\large\rm { z = 1 + 2i}$

$\large\rm { \therefore |z| = \sqrt{(1)^{2} +(2)^{2}}}$

$\large\rm { |z| = \sqrt{5}}$ .....(1)

$\large\rm { \therefore f(z) = \sqrt{ (1)^{2} + \big ( \frac{1}{2} \big ) ^{2}}}$

$\large\rm { = \frac{\sqrt{5}}{2}}$

$\large\rm { = \frac{|z|}{2}}$ from (1)

$\large\boxed{\bf { \therefore f(z) = \frac{|z|}{2}}}$