Consider four complex numbers $z_{1} = 2 + 2 i, z_{2} = 2 - 2 i, z_{3} = - 2 - 2 i, z_{4} = - 2 + 2 i$
Statement – 1 : $z_{1}, z_{2}, z_{3} a n d z_{4}$ constitute the vertices of a square of the complex plane.
Statement – 2 : The non – zero complex numbers $z, \bar{z}, - z, - \bar{z}$ always form a square.

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Both Statement – 1 and Statement – 2 are true and Statement – 2 is not the correct
explanation of Statement – 1

Both Statement – 1 and Statement – 2 are true and Statement – 2 is the correct
explanation of Statement – 1.

Statement – 1 is true but Statement – 2 is false

Statement – 1 is false but Statement – 2 is true

answer is C.

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Detailed Solution

$A B = | z_{1} - z_{2} | = | 4 i | = 4 B C = | z_{2} - z_{3} | = | 4 | = 4 C D = | z_{3} - z_{4} | = | - 4 i | = 4 D A = | z_{4} - z_{1} | = | - 4 | = 4 A C = | z_{1} - z_{3} | = | 4 + 4 i | = 4 \sqrt{2} B D = | z_{2} - z_{4} | = | 4 - 4 i | = 4 \sqrt{2}$