A) \[x=\frac{5}{13},y=\frac{8}{13}\]
B) \[x=\frac{8}{13},y=\frac{5}{13}\]
C) \[x=\frac{5}{13},y=\frac{14}{13}\]
D) None of these
Correct Answer: C
Solution :
Equation \[(x+iy)(2-3i)=4+i\] Þ \[(2x+3y)+i(-3x+2y)=4+i\] Equating real and imaginary parts, we get \[2x+3y=4\] ......(i) \[-3x+2y=1\] ......(ii) From (i) and (ii), we get \[x=\frac{5}{13},y=\frac{14}{13}\] Aliter: \[x+iy=\frac{4+i}{2-3i}=\frac{(4+i)(2+3i)}{13}=\frac{5}{13}+\frac{14}{13}i\] .You need to login to perform this action.
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