TrojanPoem
  • TrojanPoem
Z is a complex number, a is a constant. Find the maximum and minimum value of the complex number Z notice that :
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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TrojanPoem
  • TrojanPoem
\[\left| \frac{ 1 }{ Z } + Z \right| = a\]
TrojanPoem
  • TrojanPoem
a is not equal to zero
TrojanPoem
  • TrojanPoem
It's a complex number , you can assume it's A + Bi

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TrojanPoem
  • TrojanPoem
It is.
TrojanPoem
  • TrojanPoem
No problem :D
phi
  • phi
the the max and min of what ?
TrojanPoem
  • TrojanPoem
of the complex number Z
phi
  • phi
how do we define the max of a complex number? do you mean the max magnitude ?
TrojanPoem
  • TrojanPoem
You can the maximum of A , B ( A+ Bi ) is the complex number.
TrojanPoem
  • TrojanPoem
Yeah, the magnitude
phi
  • 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
TrojanPoem
  • TrojanPoem
Hmm, do you mean that e^x ? Never heard of it :(
phi
  • 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
  • phi
exp(i theta) means \( e^{i \theta}\)
TrojanPoem
  • TrojanPoem
Oh, Got it
TrojanPoem
  • TrojanPoem
Ok now we ave e^thetai + e^-thetai

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