Question

${\huge {\red {\underline {\underline {\mathcal {♡QuEstioN♡⤵}}}}}}$
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Determine the real numbers x and y if (x-iy)(3+5i) is the conjugate of -6-24i.

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⚠️ Dᴏɴ'ᴛ Sᴘᴀᴍ ⚠️​

Answer 1

conjugate of ( - 6 -24i) = ( -6 +24i)

A/C to question ,

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

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

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

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

so,

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

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

solve eqn (1) and (2)

9x + 25x = -18 + 120

34x = 102

x = 3 put this in eqn (1)

3(3 ) + 5y = -6

5y = -15

y = -3

hence, x = 3 and y = -3

Answer 2

Answer:

Answer

Given: (x−iy)(3+5i)=

(−6−24i)

⇒(3x+5y)+i(5x−3y)=−6+24i

Equating real and imaginary parts we get

3x+5y=−6…(1)

5x−3y=24…(2)

Solve (1) and (2)

:3x(1)+5×(2) we get

34x=102⇒x=43

Substitute this value in (1) we get

9+5y=−6⇒y=

5

−15

=−3

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