A) \[\frac{{{a}^{2}}+{{b}^{2}}}{{{c}^{2}}+{{d}^{2}}}\]
B) \[\frac{a+b}{c+d}\]
C) \[\frac{{{c}^{2}}+{{d}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]
D) \[{{\left( \frac{{{a}^{2}}+{{b}^{2}}}{{{c}^{2}}+{{d}^{2}}} \right)}^{2}}\]
Correct Answer: A
Solution :
\[x+iy=\sqrt{\frac{a+ib}{c+id}}\]Þ \[x-iy=\sqrt{\frac{a-ib}{c-id}}\] Also \[{{x}^{2}}+{{y}^{2}}=(x+iy)(x-iy)=\sqrt{\frac{{{a}^{2}}+{{b}^{2}}}{{{c}^{2}}+{{d}^{2}}}}\] Þ \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=\frac{{{a}^{2}}+{{b}^{2}}}{{{c}^{2}}+{{d}^{2}}}\]
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