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find the real number 'x' and 'y' if (x-iy)(3+5i) is the conjugate of -6-24i
Consider,
(x - iy) (3 + 5i)
By opening the bracket, we get
(x - iy) (3 + 5i) = x(3 + 5i) - iy (3 + 5i)
                        = 3x +5xi - [3yi + 5y]
                        = 3x + 5xi - 3yi + 5y
                        = (3x + 5y) + (5x - 3y)i
Now,
conjugate of -6 - 24i is -6 + 24i.
(x - iy) (3 + 5i) = -6 + 24i    [given]
therefore, (3x + 5y) + (5x - 3y)i = -6 + 24i.
On equating the equation we get,
3x + 5y = -6         and 5x - 3y = 24
On solving the above two eqyations we get the value of x and y
3x + 5y = -6                 ............(1) and
5x - 3y = 24                 .............(2)

therefore, y = -3
Substituting the value of y = -3 in (1)
We get,
 3x + 5x - 3 = -6
3x - 15 = -6
3x = -6 + 15
x = 9/3 = 3
x = 3
therefore, the values are x = 3 and y = -3.


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