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Model Paper 6 — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsModel Paper 61 Mark
MCQ
If z is any complex number, then $\frac{z-\bar{z}}{2 i}$ is
  • A
    either 0 or purely imaginary
  • B
    purely imaginary
  • C
    purely real
  • D
    either 0 or purely real
✓

Answer

(c) purely real
Explanation: Let $z = x + i y$
Then $\bar{z}= x - iy$
$\therefore z-\overline{z}=(x+iy)-(x-iy)=2 iy$
Now $\frac{z-\bar{z}}{2 i}=y$
Hence $\frac{z-\bar{z}}{2 i}$ is purely real.

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