If `k>0`, `|z|=\w\=k`, and `alpha=(z-bar w)/(k^2+zbar(w))`, then `Re(alpha)` (A) 0 (B) `k/2` (C) `k` (D) None of these

If k>0,|z|=|w|=k, and alpha=(z-bar(w))/(k^(2)+zbar(w))Re(alpha)

If k>0,|z|=backslash w backslash=k, and alpha=(z-bar(w))/(k^(2)+zbar(w)) then Re(alpha)(A)0(B)(k)/(2)(C)k(D) None of these

If |z|=k and omega=(z-k)/(z+k) , then Re (omega) =

If |z-1|=|z-5| and Re(z)=k ; then evaluate k

If z in C , then Re(bar(z)^(2))= k^(2), k gt 0 , represents

For k in N , let (1)/( alpha (alpha +1) (alpha +2) .....(alpha + 20)) = sum _( k =0) ^( 20) (A _(k))/( alpha + k ), where a gt 0. Then the value of 1000 ((A _(14) + A _(15) )/( A _(13))) is equal to _________.

If arg ((z-omega)/(z-omega^(2)))=0 then prove that Re (z)=-(1)/(2)(omega and omega^(2) are non-real cube roots of unity).

For a conjugated acid-base pair the relation b//w K_(a) and K_(b)