• # question_answer  If $\frac{3x+2iy}{5i-2}=\frac{15}{8x+3iy}$, then 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$

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 $x=\pm 1,y=\pm 3$