If (1+i) x-i / 2+i + (1+2i)y+i/2-i . Find the value of x and y
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correct answer is
x=3
y=−1
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Answer
Consider the given expressions.
3+i
(1+i)x−2i
+
3−i
(2−3i)y+i
=i
3+i
x+(x−2)i
+
3−i
2y+(1−3y)i
=i
9−i
2
(x+(x−2)i)(3−i)+(2y+(1−3y)i)(3+i)
=i
x(3−i)+i(x−2)(3−i)+2y(3+i)+i(1−3y)(3+i)=(9+1)i
3x−ix+i(3x−ix−6+2i)+6y+2iy+i(3+i−9y−3yi)=10i
3x−ix+3xi−i
2
x−6i+2i
2
+6y+2iy+3i+i
2
−9yi−3yi
2
=10i
3x−ix+3xi+x−6i−2+6y+2iy+3i−1−9yi+3y=10i
4x+9y−3+2xi−7yi−13i=0
4x+9y−3+(2x−7y−13)i=0
On comparing real part and imaginary part, we get
4x+9y−3=0 …… (1)
2x−7y−13=0 …… (2)
On solving both equations, we get
x=3
y=−1
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