• Support PF! Buy your school textbooks, materials and every day products Here!

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
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179

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
1
That should be [itex]-b^2[/itex], not [itex]+b^2[/itex].
Right. Let me just go fix that.

Edit. Fixed
 
  • #4
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179
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.
 

Related Threads for: Modulus Question

  • Last Post
Replies
4
Views
1K
Replies
9
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
4K
Replies
2
Views
1K
Replies
4
Views
915
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
1K
Top