QJEEM20Madd72: JEE Main 2020 Mathematics - Class 11 JEEM20Madd72 Solution: If the four complex numbers z , z ― , z ― − 2 Re ( z ― ) and z…

Question

Verified Solution • 2025–26 Session moderate

If the four complex numbers

z, \overset{―}{z}, \overset{―}{z} - 2 Re (\overset{―}{z})

and

z - 2 R e (z)

represent the vertices of a square of side 4 units in the Argand plane, then

| z |

is equal to :

Accepted Answer

Let

z = x + i y

Length of side = 4

A B = 4

| z - \overset{―}{z} | = 4

| 2 y | = 4;

\Rightarrow

| y | = 2

B C = 4

\Rightarrow

| \overset{―}{z} - (\overset{―}{z} - 2 Re (\overset{―}{z}) | = 4

\Rightarrow

| 2 x | = 4;

\Rightarrow

| x | = 2

∴

| z | = \sqrt{x^{2} + y^{2}} = \sqrt{4 + 4} = 2 \sqrt{2}

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