Question

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

Answer 1

Let z=( x−iy )( 3+5i ) .

z=3x+5xi−3yi−5y i 2 =3x+5xi−3yi+5y =( 3x+5y )+i( 5x−3y )

Conjugate of z=−6−24i is,

z ¯ =−6+24i

Compare the real and imaginary part of above expression with z ¯ =−6+24i .

3x+5y=−6 5x−3y=24

Solve the above equations.

x=3 y=−3

Hence, the values of x and y are 3 and −3 respectively.