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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
If $\frac{c+i}{c-i}=a+i b$, where $a, b, c$ are real, then $a^2+b^2=$
  • ✓
    1
  • B
    -1
  • C
    $c^2$
  • D
    $-c^2$
✓

Answer

Correct option: A.
1
(A)
$\frac{ c + i }{ c - i }= a + ib$ $\quad\ldots(i)$
$\therefore \frac{ c - i }{ c + i }= a - ib$$\quad\ldots(ii)$
Multiplying (i) and (ii), we get
$\frac{c^2+1}{c^2+1}=a^2+b^2 \Rightarrow a^2+b^2-1$

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