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STD 11 - 4.1 complex nubers — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.1 complex nubers4 Marks
Question
If $\frac{{c + i}}{{c - i}} = a + ib$, where $a,b,c$are real, then ${a^2} + {b^2} = $
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Answer

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$.

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