Saved Bookmarks
| 1. |
If `z=x+iy` and `w=(1-iz)/(z-i)`, then `|w|=1` implies that in the complex plane(A)`z` lies on imaginary axis (B) `z` lies on real axis (C)`z` lies on unit circle (D) None of these |
|
Answer» `w = (1-iz)/(z-i)` `=>|w| = |(1-iz)|/|(z-i)|` `=>|w|^2 = |(1-iz)|^2/|(z-i)|^2` `=>|w|^2 = |(1-i(x+iy))|^2/(|(x+iy)-i|^2` `=>1^2 = |(1+y) - ix|^2/|x+(y-1)i|^2` `=>x^2+(y-1)^2 = x^2+(1+y)^2` `=>y-1 = 1+y` `=> y = 0` `:. z = x+i(0) = x` `=> z= x` So, `z` lies on real axis. |
|