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4-1.Complex numbers
easy
If $\frac{{c + i}}{{c - i}} = a + ib$, where $a,b,c$are real, then ${a^2} + {b^2} = $
A
$1$
B
$ - 1$
C
${c^2}$
D
$ - {c^2}$
Solution
(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$.
Standard 11
Mathematics