A) \[-1/5\]
B) \[~1/5\]
C) \[~1/10\]
D) \[~-1/10\]
Correct Answer: A
Solution :
\[\operatorname{Re}\left[ \frac{{{(1+i)}^{2}}}{3-i} \right]\] \[=\operatorname{Re}\left[ \left( \frac{2i}{3-i} \right)\times \left( \frac{3+i}{3+i} \right) \right]\] \[=\operatorname{Re}\left[ \frac{6i-2}{9+1} \right]\] \[=\operatorname{Re}\left[ -\frac{2}{10}+\frac{6}{10}i \right]\] \[=-\frac{1}{5}\]
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