A) \[-\frac{24}{13}+\frac{10}{13}i\]
B) \[\frac{24}{13}-\frac{10}{13}i\]
C) \[\frac{10}{13}-\frac{24}{13}i\]
D) \[\frac{10}{13}+\frac{24}{13}i\]
Correct Answer: C
Solution :
\[\frac{1-2i}{2+i}+\frac{4-i}{3+2i}\] \[=\frac{1-2i}{2+i}\times \frac{2-i}{2-i}+\frac{4-i}{3+2i}\times \frac{3-2i}{3-2i}\] \[=\frac{2-i-4i+2{{i}^{2}}}{4-{{i}^{2}}}+\frac{12-8i-3i+2{{i}^{2}}}{9-4{{i}^{2}}}\] \[=\frac{2-5i-2}{5}+\frac{12-11i-2}{13}\] \[=-i+\frac{10-11i}{13}\] \[=\frac{-13i+10-11i}{13}\] \[=-\frac{24}{13}i+\frac{10}{13}\]
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