If z is a complex number such that z - i z - 1 is purely imaginary, then the minimum value of | z - ( 3 + 3 i ) | is :

Step-by-step solution

∵ z - i z - 1 is purely imaginary. arg z - i z - 1 = π 2 + n π ; n ∈ I Geometrically, the locus of z is the circle with end points of diameter is 1 , 0   &   0 , 1 and centre is 1 2 , 1 2 .So the nearest point to 3 , 3 on the circle is A 1 , 1 . Minimum distance is A P = O P - O A = 3 2 + 3 2 - 1 2 + 1 2 = 3 2 - 2 = 2 2