Question

Find the real no of x and y
(X-iy)(3+5i) is the conjugate of (-6-24i)

Answer 1

conjugate of ( - 6 -24i) = ( -6 +24i)
A/C to question ,
(x -iy)(3 + 5i) = conjugate of ( - 6 -24i)
{x(3 + 5i) -iy(3 + 5i) } = ( - 6 +24i)
3x + 5xi -3yi +5y = (- 6 +24i)
(3x + 5y) + (5x - 3y)i = (- 6 + 24i)
so,

3x + 5y = - 6 ------(1)
5x -3y = 24 --------(2)
solve eqn (1) and (2)

9x + 25x = -18 + 120
34x = 102
x = 3 put this in eqn (1)
3(3 ) + 5y = -6
5y = -15
y = -3

hence, x = 3 and y = -3