Question:
Find the real numbers x and y if (x - iy) (3 + 5i) is the conjugate of -6 - 24i.
Answer:
Given (x - iy) (3 + 5i)
= 3x + i*5x - i*3y + 5y
= (3x+ 5y) + i(5x - 3y)
Congugate of (x - iy) (3 + 5i) = (3x+ 5y) - i(5x - 3y)
Now
(3x+ 5y) - i(5x - 3y) = -6 - 24i
Compare real and imaginary term , we get
=> 3x+ 5y = -6 ...........1
5x - 3y = 24 ...........2
After solving equation 1 and 2 , we get
x =3 and y= -3
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