A) \[x=1,y=-3\]
B) \[x=-1,y=3\]
C) \[x=1,y=3\]
D) \[x=-1,y=-3\]or \[x=1,\]\[y=3\]
Correct Answer: D
Solution :
Given that \[\frac{3x+2iy}{5i-2}=\frac{15}{8x+3iy}\] Þ \[24{{x}^{2}}+9ixy-6{{y}^{2}}+16ixy=75i-30\] Þ \[24{{x}^{2}}-6{{y}^{2}}+25ixy=75i-30\] Equating real and imaginary parts, we get \[24{{x}^{2}}-6{{y}^{2}}=-30\]or \[4{{x}^{2}}-{{y}^{2}}=-5\]and \[xy=3\] On solving we get \[x=\pm 1,y=\pm 3\]
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