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Complex Plane

Source: 1992 National High School Mathematics League, Exam One, Problem 5

February 26, 2020
complex numbersgeometry

Problem Statement

Points on complex plane that complex numbers z1,z2z_1,z_2 corresponding to are A,BA,B, and ∣z1∣=4,4z12−2z1z2+z22=0|z_1|=4,4z_1^2-2z_1z_2+z_2^2=0. OO is original point, then the area of △OAB\triangle OAB is (A)83(B)43(C)63(D)123\text{(A)}8\sqrt3\qquad\text{(B)}4\sqrt3\qquad\text{(C)}6\sqrt3\qquad\text{(D)}12\sqrt3
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