A) \[\frac{13}{5}\]
B) \[\frac{11}{5}\]
C) \[\frac{9}{5}\]
D) \[\frac{7}{5}\]
Correct Answer: A
Solution :
[a] \[\because z={{\frac{(3+2i)}{4-3i}}^{2}}=\frac{9-4+12i}{4-3i}\] \[=\frac{5+12i}{4-3i}\times \frac{4\times 3i}{4\times 3i}=\frac{20-36+63i}{{{(4)}^{2}}+{{(3)}^{2}}}=\frac{-16+63i}{25}=\left( \frac{-16}{25} \right)+\left( \frac{63}{25} \right)i\] \[\left| z \right|=\sqrt{{{\left( \frac{-16}{25} \right)}^{2}}+{{\left( \frac{63}{25} \right)}^{2}}}=\sqrt{\frac{256+3936}{625}}=\frac{65}{25}=\frac{13}{5}\] Hence, option [a] is correct
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