Question

Find the value of x and y if (x-iy) (3+5i)=-6+24i

Answer 1

Answer:

The values of x and y are 3 & - 3 respectively.

Step-by-step-explanation:

We have given that,

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

We have to find the value of x and y.

Now,

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

⇒ x ( 3 + 5i ) - iy ( 3 + 5i ) = - 6 + 24i

⇒ 3x + 5xi - 3iy - 5i²y = - 6 + 24i

We know that,

i² = - 1

⇒ 3x + 5xi - 3iy - 5 * ( - 1 ) * y = - 6 + 24i

⇒ 3x + 5xi - 3iy + 5y = - 6 + 24i

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

By comparing both sides, we get,

3x + 5y = - 6 - - - ( 1 )

5x - 3y = 24 - - - ( 2 )

Multiplying equation ( 1 ) by 3 and equation ( 2 ) by 5, we get,

3 ( 3x + 5y ) = - 6 * 3

⇒ 9x + 15y = - 18 - - - ( 3 )

And,

5 ( 5x - 3y ) = 5 * 24

⇒ 25x - 15y = 120 - - - ( 4 )

By adding equations ( 3 ) & ( 4 ), we get,

9x + 15y + ( 25x - 15y ) = - 18 + 120

⇒ 9x + 15y + 25x - 15y = 102

⇒ 9x + 25x + 15y - 15y = 102

⇒ 34x = 102

⇒ x = 102 ÷ 34

⇒ x = 3

By substituting x = 3 in equation ( 1 ), we get,

3x + 5y = - 6 - - - ( 1 )

⇒ 3 * 3 + 5y = - 6

⇒ 9 + 5y = - 6

⇒ 5y = - 6 - 9

⇒ 5y = - 15

⇒ y = - 15 ÷ 5

⇒ y = - 3

∴ The values of x and y are 3 & - 3 respectively.