"Solve the equation 2*z = z + 2*i , for any complex number z "
My working out thus far consists of writing out z in terms of its imaginary/real parts(A + B*i) and z as sqrt(A^2 + B^2) and then equating the real and imaginary parts of both sides. Although, I think this is the entirely wrong direction anyway.
Any help would be appreciated .

Mr.bob
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 10012017 10:39
Last edited by Mr.bob; 10012017 at 10:40. 
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ghostwalker
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 10012017 10:52
(Original post by Mr.bob)
"Solve the equation 2*z = z + 2*i , for any complex number z "
My working out thus far consists of writing out z in terms of its imaginary/real parts(A + B*i) and z as sqrt(A^2 + B^2) and then equating the real and imaginary parts of both sides. Although, I think this is the entirely wrong direction anyway.
Any help would be appreciated .
What have you got, thus far? 
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 10012017 10:58
(Original post by ghostwalker)
Equating imaginary parts is sufficient to get you B, since z is real.
What have you got, thus far?
The problem is i dont really understand what the question is looking for 
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 10012017 11:02
(Original post by Mr.bob)
yeah i found B to be 1, then substituted this into the expression "2*A = sqrt(A*2 + B*2)" to find A(which i found to be sqrt(1/3)).
The problem is i dont really understand what the question is looking for 
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 10012017 11:08
(Original post by ghostwalker)
You're looking for the value of z, and since you have z=A+iB, and you know what A,B are, ...
This is what i had for my answer but im just uncertain how this satisfies what the question was asking 
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 10012017 11:18
(Original post by Mr.bob)
so Z = +/sqrt(1/3) + i
This is what i had for my answer but im just uncertain how this satisfies what the question was asking
I presume that at one point in your working you squared an equation. This can introduce additional solutuions that don't satisfy the original equation. So, you need to check each solution to make sure it does.
The original question is poorly worded, IMO. If it had just said "solve the equation ..." and left it at that, it would have made more sense. 
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 10012017 11:28
(Original post by ghostwalker)
You initially said A=sqrt(1/3), but now you've put +/ that.
I presume that at one point in your working you squared an equation. This can introduce additional solutuions that don't satisfy the original equation. So, you need to check each solution to make sure it does.
The original question is poorly worded, IMO. If it had just said "solve the equation ..." and left it at that, it would have made more sense. 
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 10012017 11:29
(Original post by Mr.bob)
"Solve the equation 2*z = z + 2*i , for any complex number z "
My working out thus far consists of writing out z in terms of its imaginary/real parts(A + B*i) and z as sqrt(A^2 + B^2) and then equating the real and imaginary parts of both sides. Although, I think this is the entirely wrong direction anyway.
Any help would be appreciated .
Edit: easier: note that allows you to write down a quadratic equation for , which then immediately gives you the solutions forLast edited by atsruser; 10012017 at 11:51. 
Mr.bob
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 10012017 11:53
(Original post by atsruser)
One approach is to note that so that is a real number since it is equal to , which is a real number.
Edit: easier: note that allows you to write down a quadratic equation for , which then immediately gives you the solutions for 
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 10012017 12:25
(Original post by Mr.bob)
yeah, the approach i used results in the same imaginary part being found as this method(that being equal to 1). What about the real part though? 
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 10012017 17:19

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 10012017 17:56
(Original post by Mr.bob)
but how do i find z
So we have with
Now write down z in terms of a and b, and hence in terms of what they equal. You will then have an equation in z to solve.
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