It is known that the complex numbers of vertices a and B of isosceles trapezoid oabc on the complex plane are 1 + 2I and - 2 + 6I respectively, and O is the origin of coordinates, OA ‖ BC. Find the complex number Z corresponding to vertex C

It is known that the complex numbers of vertices a and B of isosceles trapezoid oabc on the complex plane are 1 + 2I and - 2 + 6I respectively, and O is the origin of coordinates, OA ‖ BC. Find the complex number Z corresponding to vertex C

Let C (x, y) be an isosceles trapezoid, then we can get | OC | = | ab | and OA ∥ BC, ｜ x2 + y2 = (− 2 − 1) 2 + (6 − 2) 2Y − 6 = 2 (x + 2), and we can get the complex number z = - 5 corresponding to vertex C

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