Question

(x+2iy)(x-5iy)/(-x+3iy)(x+iy)​

Answer 1

Answer:

$\frac{(x + 2iy)(x - 5iy)}{( - x + 3iy)(x + iy)} \\ = \frac{x (x - 5iy) +2iy (x - 5iy)}{- x (x + iy) + 3iy(x + iy)} \\ = \frac{x^{2} - 5ixy +2ixy - 10i^{2} y^{2} }{- x^{2} - ixy + 3ixy +3 i ^{2} y ^{2}} \\ = \frac{ {x^{2} - 3ixy - 10( - 1)y}^{2} }{ - {x}^{2} + 2ixy + 3( - 1) {y}^{2} } \\ = \frac{ {x^{2} - 3ixy + 10y^{2}} }{ - {x}^{2} + 2ixy - 3{y}^{2} } \\ = \frac{ {x^{2} + 10y^{2}} \: - 3ixy }{ - {x}^{2} - 3{y}^{2} + 2ixy } \:$