ABCD is a square with the letters in the anti-clockwise order. The points A and B represents 2+3i and 6+i respectively. Find the complex numbers represented by C and D.
Since the complex number 2 + 3i means A = (2, 3) in space and 6 + i represents B (6, 1) in space, graph these points.
Rule: `a+bi = (a, b)`
The slope between these 2 points is `-1/2` so slope between B anc C must be `2.`
Since points must be counter-clockwise, the point C would be "northeast" of B. Keeping with perpendicular slope and the same distance between A and B to form a square, C would be at (8, 5) and D will be at (4, 7).
Therefore point C would be represented by the complex number `8 + 5i.`
Point D at (4, 7) would be represented by the complex number `4+7i.`
C = 8+5i and D = 4+7i