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

Marks : 06

Years : MAY 2016

$$\dfrac {(w-w_1)}{(w_1-w_2)} \dfrac{(w_2-w_3)}{(w_3-w)} = \dfrac {(z-z_1)}{(z_1-z_2)} \dfrac{(z_2-z_3)}{(z_3-z)} $$

$\dfrac {(w-i)}{(i-0)} \dfrac {(0+i)}{(-i-w)} =\dfrac {(z-1)(i+1)}{(1-i)(-1-z)} \therefore \Rightarrow \dfrac {(w-i)}{(w+i)} =\dfrac {(z-1)(i+1)}{(z+1)(1-i)} \\ \Rightarrow \dfrac {w-i}{w+i} =\dfrac {(z-1)(1+2i-1)}{(z+1)(2)} =\dfrac {(z-1)i}{(z+1)} $

By dividendo & componendo method $\dfrac {D+N}{D-N}$

$ \dfrac {2w}{2i} =\dfrac {(z+1)+zi-i}{(z+1)-zi+i} = \dfrac {z(1+i) -i(1+i)}{-zi(1+i) + 1(1+i)} \\ \dfrac wi =\dfrac {z-i}{-zi+1}\Rightarrow W=\dfrac {zi+1}{-zi+1} \space or \space w =\dfrac {z-i}{-z-i}$