MHT CET20243 May 2024Morning ShiftMathematicsComplex NumberActual
If |z|=1 and w= z-1 z+1 (where z -1 ), then Re ( w ) is
Options
- A0
- B- 1 |z+1|^2
- C| z z+1 | 1 |z+1|^2
- D2 |z+1|^2
Correct answer
A. 0
Step-by-step solution
aligned W & = z -1 z +1 & = x+ i y-1 x+ i y+1 & = (x-1+ i y) (x+1+ i y) (x+1- i y) (x+1- i y) aligned aligned & = (x^2+y^2-1 )+(-x y+1+x y+1) i (x+1)^2+y^2 & = x^2+y^2+1 (x+1)^2+y^2 + 2 y i (x+1)^2+y^2 aligned Given that |z|=1 aligned & x^2+y^2=1 & x^2+y^2-1=0 aligned Re ( w )=0