1. Tardigrade
  2. Question
  3. Mathematics
  4. 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 12= z 2 z 3 and z 22= z 3 z 1 then which of the following is/are correct.

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Q. 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.

Complex Numbers and Quadratic Equations

Solution:

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) $(3) \Rightarrow(2)$