Modulus Question

  • #1
353
1

Homework Statement


Find all ##z=a+bi## such that:
[tex]|z|=|z^{2}+1|[/tex]


Homework Equations





The Attempt at a Solution


I expanded the components.
[tex]|z|=|z^{2}+1|[/tex]
[tex]z^{2}=a^2-b^2+2abi[/tex]
[tex]\sqrt{a^{2}+b^{2}}=\sqrt{(a^{2}-b^{2}+1)^{2}+(2ab)^{2}}[/tex]
[tex]a^2+b^2=(a^{2}-b^{2}+1)^{2}+(2ab)^{2}[/tex]
[tex]0=a^{4}+2a^{2}b^{2}+b^{4}+a^{2}-3b^{2}+1[/tex]

I don't see what to do now...
 
Last edited:

Answers and Replies

  • #2
jbunniii
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Homework Statement


Find all ##z=a+bi## such that:
[tex]|z|=|z^{2}+1|[/tex]


Homework Equations





The Attempt at a Solution


I expanded the components.
[tex]|z|=|z^{2}+1|[/tex]
[tex]z^{2}=a^2+b^2+2abi[/tex]
That should be [itex]-b^2[/itex], not [itex]+b^2[/itex].
 
  • #3
353
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That should be [itex]-b^2[/itex], not [itex]+b^2[/itex].

Right. Let me just go fix that.

Edit. Fixed
 
  • #4
jbunniii
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Right. Let me just go fix that.

Edit. Fixed

Well, you fixed it in the first line where it appeared, but you still need to fix it everywhere else.
 
  • #5
353
1
Well, you fixed it in the first line where it appeared, but you still need to fix it everywhere else.

I fixed then end before, I just forgot to change the middle parts.
 

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