Question

Find the value of X and Y , if

(3x - 2iy)(2 + I)² = 10(1 + i).


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Answer 1

HƏÝĀ MÅÞƏ.......☺

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3x - 2iy)(2+i)2 = 10 (1+ i)

( 3x - 2iy )(4+i2+4i)= 10 + 10i

(3x -2iy) (3+4i) = 10 + 10i

(3x- 2iy)= 10+ 10i / 3+4i

3x - 2iy = 10(7+i)/25

3x-2iy = 14 + 7i/5

15x - 10iy = 14 + 7i

on comparing we get...

15x = 14

x = 14/15

and........-10iy = 7i

y = 7/10..

×=×=×=×=×=×=×=×=×=×

HOPE THIS HELPS YOU

Answer 2

$\huge\mathfrak{Heya\: Mate}$

$\huge\bold{Solution}$

We have ,

(3x - 2iy) (2 + i)² = 10(1 + i)

=> (3x - 2iy) ( 4 + i² + 4i) = 10 + 10i

=> (3x - 2iy) ( 4 - 1 + 4i) = 10 + 10i

=> (3x - 2iy) (3 + 4i) = 10 + 10i

=> 9x + 8y + i (12x - 6y) = 10 + 10i

On equating real and imaginary parts both sides , we get

9x + 8y = 10....(i)

12x - 6y = 10....(ii)

on solving Eq (i) & (ii), we get

x = 14/15

and

y = 1/5

Hope it helps you out✔✔✔