A) 1
B) \[-1\]
C) \[{{c}^{2}}\]
D) \[-{{c}^{2}}\]
Correct Answer: A
Solution :
\[\frac{c+i}{c-i}=a+ib\] .....(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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