A) \[0\]
B) \[-1\]
C) \[2i\]
D) \[-2i\]
Correct Answer: C
Solution :
\[\frac{\alpha }{a}+\frac{\beta }{b}+\frac{\gamma }{c}=1+i\] squaring \[\frac{{{\alpha }^{2}}}{{{a}^{2}}}+\frac{{{\beta }^{2}}}{{{b}^{2}}}+\frac{{{\gamma }^{2}}}{{{c}^{2}}}+2\left( \frac{\alpha \beta }{ab}+\frac{\beta \gamma }{bc}+\frac{\gamma \alpha }{ac} \right)=2i\] or \[\frac{{{\alpha }^{2}}}{{{a}^{2}}}+\frac{{{\beta }^{2}}}{{{b}^{2}}}+\frac{{{\gamma }^{2}}}{{{c}^{2}}}+\frac{2\alpha \beta \gamma }{abc}\left( \frac{c}{\gamma }+\frac{a}{\alpha }+\frac{b}{\beta } \right)=2i\] \[\therefore \,\,\,\frac{{{\alpha }^{2}}}{{{a}^{2}}}+\frac{{{\beta }^{2}}}{{{b}^{2}}}+\frac{{{\gamma }^{2}}}{{{c}^{2}}}=2i\]
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