# Vector question: Explanation on “what to do to solve it?”

**Question**

Consider a complex number (z=x+yj) in the “complex plane” to be a vector. The vertices of a triangle A, B, and C are given by the complex numbers 1+j, 2-j, and -1 respectively. Find the point that is equidistant to A, B, and C.

**Answer**

z=x+yj is (x,y) and the points (1,1) , (2,-1) and (-1,0) respectively.

Let the distance be called D.

D^2 = (x -1)^2 + (y – 1)^2 ..(1)

D^2 = (x -2)^2 + (y +1)^2 ….(2)

D^2 = (x +1)^2 + y ^2 ….(3)

3 equations and 3 unknowns… Solve it simulteneously and you are done.