Statement-1 (Assertion) and Statement-2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You
\( \mathrm{P} \) have to select the correct choice as given below.
W
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(c) Statement1 is true, Statement-2 is false
(d) Statement-1 is false, Statement-2 is true
Statement-1 Let \( z_{1}, z_{2} \) and \( z_{3} \) be three complex numbers, such that \( \left|3 z_{1}+1\right|=\left|3 z_{2}+1\right|=\left|3 z_{3}+1\right| \) and \( 1+z_{1}+z_{2}+z_{3}=0 \), then \( z_{1}, z_{2}, z_{3} \) will represent vertices of an equilateral triangle on the complex plane.
Statement-2 \( z_{1}, z_{2} \) and \( z_{3} \) represent vertices of an equilateral triangle, if
\[
z_{1}^{2}+z_{2}^{2}+z_{3}^{2}+z_{1} z_{2}+z_{2} z_{3}+z_{3} z_{1}=0
\]
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