Question

Let $z_1,z_2,z_3$ are three non zero complex numbers denoting the vertices of an equilateral triangle $A_1,A_2,A_3$ respectively.
Consider the statements
(1) $A_1{A}_2{A}_3$ is an equilateral triangle.
(2) $z_1{\overline{z}}_2=z_2{\overline{z}}_3=z_3{\overline{z}}_1$
(3) $z_1^2=z_2{z}_3$ and $z_2^2=z_3{z}_1$
then which of the following is/are correct.

• A. $(2)\Rightarrow (1)$
• B. $(3)\Rightarrow (1)$
• C. $(2)\Rightarrow (3)$
• D. $(3)\Rightarrow (2)$

Answer 1

Answer: (A), (B), (C), (D)

Correct answer is (a) $(2)\Rightarrow (1)$ Correct answer is (b) $(3)\Rightarrow (1)$ Correct answer is (c) $(2)\Rightarrow (3)$ Correct answer is (d) $(3)\Rightarrow (2)$