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.

Expert Answers
baxthum8 eNotes educator| Certified Educator

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

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