Quadratic equation

Question

Find real x and y if (x − iy) (3 + 5i) is the conjugate of −6 − 24i

Answer 1

The conjugate of -6 - 24i is -6 + 24i.

It is given that -6 + 24i = (x – iy) (3 + 5i)

-6 + 24i = 3x + 5xi - 3iy - 5yi²

-6 + 24i = (3x + 5y) + i (5x - 3y)

Comparing the real and imaginary parts,

3x + 5y = -6 

5x - 3y = 24

Solving these two equations we get x = 3 and y = -3.

Therefore, x = 3 and y = -3.