Question bank/JEE Main/Mathematics

If z_1, z_2, z_3 are three points lying on the circle |z| =
2 then the minimum value of
$\left| z_{1} + z_{2} \right|^{2} + \left| z_{2} + z_{3} \right|^{2}\left| z_{3} + z_{1} \right|^{2}$
is equal to

A6B12C15D24

Show answer and solution▾

$\left| z_{1} + z_{2} \right|^{2} + \left| z_{2} + z_{3} \right|^{2} + \left| z_{3} + z_{1} \right|^{2}$
$\mathbf{=}2\left( \left| z_{1} \right|^{2} + \left| z_{2} \right|^{2} + \left| z_{3} \right|^{2} \right)$+$\left( z_{1}\overrightarrow{z_{2}} + z_{2}\overrightarrow{z_{1}} + z_{2}\overrightarrow{z_{3}} + z_{3}\overrightarrow{z_{2}} + z_{3}\overrightarrow{z_{1}} + z_{1}\overrightarrow{z_{3}} \right)$

Source: Grass-G / M-23 Mathematics Paper 31 Dec FST.docx