MCQ
If $\frac{{c + i}}{{c - i}} = a + ib$, 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
(a) $\frac{{c + i}}{{c - i}} = a + ib$.....$(i)$
$\frac{{c + i}}{{c - i}} = a + ib$.....$(ii)$
Multiplying $(i)$ and $(ii)$, we get
$\frac{{{c^2} + 1}}{{{c^2} + 1}} = {a^2} + {b^2}$ $ \Rightarrow {a^2} + {b^2} = 1$.
(a) $\frac{{c + i}}{{c - i}} = a + ib$.....$(i)$
$\frac{{c + i}}{{c - i}} = a + ib$.....$(ii)$
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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