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

Q: 14     Find the real numbers x andy if  \small (x-iy)(3+5i) is the conjugate of  \small -6-24i.

Answers (1)

best_answer

Let 
z = \small (x-iy)(3+5i) = 3x+5xi-3yi-5yi^2= 3x+5y+i(5x-3y)
Therefore,
\bar z = (3x+5y)-i(5x-3y) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -(i)
Now, it is given that 
\bar z = -6-24i \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -(ii)
Compare (i) and (ii) we will get
(3x+5y)-i(5x-3y) = -6-24i
On comparing real and imaginary part. we will get
3x+5y=-6 \ \ \ and \ \ \ 5x-3y = 24
On solving these we will get
x = 3 \ \ \ and \ \ \ y =- 3

Therefore, the value of x and y are 3 and -3 respectively

Posted by

Gautam harsolia

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