# Complex number

by sharks
Tags: complex, number
 PF Gold P: 836 The problem statement, all variables and given/known data Given that the real and imaginary parts of the complex number $z=x+iy$ satisfy the equation $(2-i)x-(1+3i)y=7$. Find x and y. The attempt at a solution I know it's quite simple. Just equate the real and imaginary parts, but i checked and redid it again, but the answer still evades me! $$(2x-y-7) + i(-x-3y)=0 \\2x-y-7=x \\x-y=7\, (1) \\-x-3y=y \\4y+x=0\, (2) \\x=28/5 \\y=-7/5$$ I replaced in the original equation but i can't get 7 on the L.H.S. The correct answers: x=3 and y=-1.
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PF Gold
P: 7,721
 Quote by sharks The problem statement, all variables and given/known data Given that the real and imaginary parts of the complex number $z=x+iy$ satisfy the equation $(2-i)x-(1+3i)y=7$. Find x and y. The attempt at a solution I know it's quite simple. Just equate the real and imaginary parts, but i checked and redid it again, but the answer still evades me! $$(2x-y-7) + i(-x-3y)=0 \\2x-y-7=x \\x-y=7\, (1) \\-x-3y=y \\4y+x=0\, (2) \\x=28/5 \\y=-7/5$$ I replaced in the original equation but i can't get 7 on the L.H.S. The correct answers: x=3 and y=-1.
Why aren't those 0 on the right side?
Emeritus
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PF Gold
P: 7,819
 Quote by sharks Given that the real and imaginary parts of the complex number $z=x+iy$ satisfy the equation $(2-i)x-(1+3i)y=7$. Find x and y. $$(2x-y-7) + i(-x-3y)=0 \\2x-y-7=x \\ \dots \\-x-3y=y \\ \dots$$
When you write:
$2x-y-7=x$

and

$-x-3y=y\ ,$
you are saying that
$(2x-y-7) + i(-x-3y)=z\ .$
That's not what you're trying to solve !

 PF Gold P: 836 Complex number I was confused about z=x+iy. I thought i had to compare the real and imaginary parts of z with those of the equation in order to solve it. I now realize that it has absolutely nothing to do with z. All i had to do was solve the equation independently and ignore whatever was given for z. Solving:$$2x-y=7 \\-x-3y=0$$I get the correct answers. Thank you, LCKurtz and SammyS.

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