If z=2+i, then (z-1)( barz-5)+( barz-1)(z-5) is equal to

Question

If z=2+i, then (z-1)( barz-5)+( barz-1)(z-5) is equal to (A) 2 (B) 7 (C) -1 (D) -4

Tardigrade Admin · Accepted Answer

(z-1)( barz-5)+( barz-1)(z-5) =2Re[(z-1)( barz-5)] (∵ z1 barz2+z2 barz1=2Re(z1 barz2)) =2 Re [(1+i)(-3-i)]=2(-2)=-4 (Given z = 2 +i)

Q. If $z = 2 + i$ , then $(z - 1) (\overset{z}{ˉ} - 5) + (\overset{z}{ˉ} - 1) (z - 5)$ is equal to