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JEE Main 20205 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
5 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Complex Number

JEE Main 2020 · 5 September · Morning Shift · Mathematics · Complex Number

If the four complex numbers z, ¯ z , ¯ z - 2 Re ( ¯ z ) and z - 2...

If the four complex numbers z,z¯,z¯−2Re(z¯)z, \overset{¯}{z}, \overset{¯}{z} - 2 Re \left(\overset{¯}{z}\right) and z - 2 Re\left(z\right)representtheverticesofasquareofsiderepresent the vertices of a square of side4unitsintheArgandplane,then∣z∣units in the Argand plane, then \left|z\right| is equal to :If the four complex numbers z, ¯ z , ¯ z - 2 Re ( ¯ z ) and z - 2 Re(z) represent the vertices of a square of side 4

Options

  1. A424\sqrt{2}
  2. B44
  3. C222\sqrt{2}
  4. D22

Correct answer

C. 222\sqrt{2}

Step-by-step solution

Let z=x+iyz = x + iy

If the four complex numbers z, ¯ z , ¯ z - 2 Re ( ¯ z ) and z - 2 Re(z) represent the vertices of a square of side 4

∴∴ length of side =4= 4

then \left|z - \overset{¯}{z}\right| = 4</p><p>∣2iy∣=4</p><p>\left|2iy\right| = 4

\left|y\right| = 2</p><p>also∣z−(z−2Re(z))∣=4</p><p>also \left|z - \left(z - 2 Re \left(z\right)\right)\right| = 4

\left|2x\right| = 4 ⇒ \left|x\right| = 2</p><p>∣z∣=x2+y2=22</p><p>\left|z\right| = \sqrt{{x}^{2} + {y}^{2}} = 2\sqrt{2}

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