AP EAMCET202318 May 2023Evening ShiftMathematicsComplex NumberActual
If z=1+ -i and 0 < < , then [|z-1|^2- |z|^2 4 ]^ 1 / 2 =
Options
- A2
- B2
- C( 2 )
- D( 2 )
Correct answer
D. ( 2 )
Step-by-step solution
aligned & Since, Z=1+ -i & z-1= -i & |z-1|= |e^ i |=1 & Now, |z|= (1+ )^2+ ^2 = 2+2 & [|z-1|^2- |z|^2 4 ]^ 1 2 = [1- 1+ 2 ]^ 1 2 = [ 1- 2 ]^ 1 2 & [|z-1|^2- |z|^2 4 ]^ 1 2 = [ 1-1+2 ^2 2 2 ]^ 1 / 2 = 2 aligned