If Z - 2 = 2 Z - 1 , then the value of R e Z Z 2 is (where Z is a complex number and Re( Z ) represents the real part of Z )

Question

If Z - 2 = 2 Z - 1 , then the value of R e Z Z 2 is (where Z is a complex number and Re( Z ) represents the real part of Z ),

MARKS App · Accepted Answer

Let, Z = x + i y ⇒ x - 2 + i y = 2 x - 1 + i y ⇒ x - 2 2 + y 2 = 4 x - 1 2 + y 2 ⇒ 3 x 2 + y 2 - 4 x = 0 ⇒ x x 2 + y 2 = 3 4 ⇒ R e Z Z 2 = 0 . 7 5