For a complex number Z , if the argument of 3 + 3 i and Z - 2 Z - - 1 are equal, then the maximum distance of Z from the x -axis is equal to (where, i 2 = - 1 )

Step-by-step solution

Let, Z = x + i y Now, Z - 2 Z - - 1 = Z Z - - 2 Z - - Z + 2 = x 2 + y 2 - 3 x + 2 + i y a r g of 3 + 3 i = π 4 ⇒ x 2 + y 2 - 3 x + 2 = y   where   y > 0 ⇒ x 2 + y 2 - 3 x - y + 2 = 0 Centre of the circle is 3 2 , 1 2 and radius = 1 2 ⇒ required value = 1 2 + 1 2 units