Question

if find the value of x and y if (x-iy) (2+ 5i) = 9+8i​

Answer 1

(x-iy) (2+ 5i) = 9+8i

=> 2x+5xi-2iy+5y = 9+8i

=> (2x+5y) + i ( 5x-2y) = 9+8i

Now,

Equatting real and imaginary parts we get -

2x+5y =9 ....... (i) and , 5x-2y=8.....(ii)

(i) + (ii) => 7x-3y = 17

=> 7x = 17+3y

=> x = ( 17+3y) / 7 ..........(iii)

(i) => 2× ( 17+3y) / 7 + 5y = 9

=> (34+41y)/7 = 9

=> 41y = 29

=> y = 29/41

Now,

(iii) => x = ( 17 +3×29/41)/ 7

={( 697+87)/41} / 7

= 784/ 7×41

= 784/287

Hence, x= 784/287 and , y = 29/41