A) \[\frac{13}{2}+i\,\left( \frac{15}{2} \right)\]
B) \[\frac{13}{10}+i\left( \frac{-15}{2} \right)\]
C) \[\frac{13}{10}+i\,\left( \frac{-9}{10} \right)\]
D) \[\frac{13}{10}+i\,\left( \frac{9}{10} \right)\]
Correct Answer: C
Solution :
\[z=\frac{{{(2+i)}^{2}}}{3+i}\]\[=\frac{3+4i}{3+i}\times \frac{3-i}{3-i}\]\[=\frac{13}{10}+i\frac{9}{10}\] Conjugate\[=\frac{13}{10}-i\frac{9}{10}\].
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