Question

(x+i y)/(2+3i)+(2+i)/2-3i=9/13(1+i) find value of x and y​

Answer 1

x+iy/2+3i+2+i/2-3i=9/13(1+i)

(x+yi)(2-3i)+(2+i)(2+3i)/(2+3i)(2-3i)=9/13(1+i)

2x-3xi+2yi-3yi²+4+6i+2i+3i²/4-9i=9+9i/13

2x-3xi+2yi+3y+4+8i-3/13=9+9i/13

(2x+3y+1)+(8-3x+2y)I=9+9i

2x+3y+1=9 and 8-3x+2y=9

3x-2y=-1

question 1 multiply by 2 and in equation 2 x 3

13x=13 ,x=2

putting x=1 in equation 1 we get

2(1)+3y=8

3y=6

y=2

answer is, x=1 and y=2

Answer 2

Answer:

x+iy/2+3i+2+i/2-3i=9/13(1+i)

(x+yi)(2-3i)+(2+i)(2+3i)(2+3i)(2-3i)=9/13(1+i)

2x-3xi+2yi-3yi2+4+6i+2i+3i2/4-9i=9+91/13

2x-3xi+2yi+3y+4+8i-3/13=9+9i/13

(2x+3y+1)+(8-3x+2y)=9+9i

2x+3y+1=9 and 8-3x+2y=9

3x-2y=-1question 1 multiply by 2 and in equation 2

x 3

13x=13 ,x=2

putting x=1 in equation 1 we get

2(1)+3y=8

3y=6

y=2

answer is, x=1 and y=2

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