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Complex number

by sharks
Tags: complex, number
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sharks
#1
Apr28-12, 03:42 PM
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The problem statement, all variables and given/known data
Given that the real and imaginary parts of the complex number [itex]z=x+iy[/itex] satisfy the equation [itex](2-i)x-(1+3i)y=7[/itex]. 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!
[tex](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
[/tex]
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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LCKurtz
#2
Apr28-12, 03:57 PM
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Quote Quote by sharks View Post
The problem statement, all variables and given/known data
Given that the real and imaginary parts of the complex number [itex]z=x+iy[/itex] satisfy the equation [itex](2-i)x-(1+3i)y=7[/itex]. 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!
[tex](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
[/tex]
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?
SammyS
#3
Apr28-12, 04:48 PM
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Quote Quote by sharks View Post
Given that the real and imaginary parts of the complex number [itex]z=x+iy[/itex] satisfy the equation [itex](2-i)x-(1+3i)y=7[/itex]. Find x and y.

[tex](2x-y-7) + i(-x-3y)=0
\\2x-y-7=x
\\ \dots
\\-x-3y=y
\\ \dots [/tex]
When you write:
[itex]2x-y-7=x[/itex]

and

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

sharks
#4
Apr28-12, 08:27 PM
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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:[tex]2x-y=7
\\-x-3y=0[/tex]I get the correct answers.

Thank you, LCKurtz and SammyS.


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