Mumbai university > Electronics and telecommunication engineering, Electronics engineering > Sem 3 > Applied mathematics 3

Marks : 06

Years : MAY 2016

$$w=\dfrac {i-iz}{1+z} \Rightarrow w+wz+iz=i $$

$ \Rightarrow z(i+w) =i-2\Rightarrow z=\dfrac {i-w}{i+z} \\ But \space |z|=1\Rightarrow \Bigg| \dfrac {i-w}{i+z}\Bigg| =1 , \Rightarrow \Bigg|\dfrac {i-(u+iv)}{i+(u+iv)}\Bigg| =1 \\ |-u+i(-v+1)| =|u+i(v+1)| \\ u^2+v^2 -2v+1 = u^2+v^2+2v+1 \\ 4v=0 \\ v=0 \Rightarrow \text { Real axis of w-plane}$