Z is a complex number, a is a constant. Find the maximum and minimum value of the complex number Z notice that :

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Z is a complex number, a is a constant. Find the maximum and minimum value of the complex number Z notice that :

Mathematics
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\[\left| \frac{ 1 }{ Z } + Z \right| = a\]
a is not equal to zero
It's a complex number , you can assume it's A + Bi

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Other answers:

It is.
No problem :D
  • phi
the the max and min of what ?
of the complex number Z
  • phi
how do we define the max of a complex number? do you mean the max magnitude ?
You can the maximum of A , B ( A+ Bi ) is the complex number.
Yeah, the magnitude
  • phi
you could write Z= a exp( i x) so Z+1/Z = a exp(ix) + (1/a) exp(-ix) and the magnitude squared is | Z+1/Z |^2 = (a exp(ix) + (1/a) exp(-ix))(a exp(-ix) + (1/a) exp(ix)) which might lead to a solution
Hmm, do you mean that e^x ? Never heard of it :(
  • phi
no. I meant a complex number in polar coords is magnitude * exp( i* theta) btw, I should have used r instead of a, to not confuse the magnitude with the "a" given in your problem.
  • phi
exp(i theta) means \( e^{i \theta}\)
Oh, Got it
Ok now we ave e^thetai + e^-thetai

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