A) \[\frac{13}{2}+i\left( \frac{15}{2} \right)\]
B) \[\frac{13}{10}+\left( \frac{-15}{2} \right)i\]
C) \[\frac{13}{10}+i\left( \frac{9}{10} \right)\]
D) none of these
Correct Answer: C
Solution :
\[=\frac{{{(2+i)}^{2}}}{3+i}=\frac{4+{{i}^{2}}+4i}{3+i}\] \[=\frac{3+4i}{3+i}\times \frac{3-i}{3-i}=\frac{9+12i-3i-4{{i}^{2}}}{9-{{i}^{2}}}\] \[=\frac{13+9i}{10}=\left( \frac{13}{10} \right)+i\left( \frac{9}{10} \right)\]
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