Simplify Tricky Equation for Purely Imaginary C with Complex Constants

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Discussion Overview

The discussion revolves around solving an equation for a purely imaginary value C, where C is influenced by complex constants F and G. The focus is on the methods to isolate C and simplify the equation, with participants providing hints and approaches for tackling the problem.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant seeks advice on isolating C in the equation involving complex constants.
  • Another participant suggests taking logarithms of both sides as a potential method to solve for C.
  • A third participant proposes a change of variables, defining A and B to simplify the equation further.
  • Some participants express confidence that the hints provided will lead to an easy solution for C.
  • One participant confirms they have successfully worked out the solution after receiving hints.
  • A later reply inquires about the origin of the equation being discussed.

Areas of Agreement / Disagreement

Participants generally agree on the methods suggested for solving the equation, but the discussion does not reach a consensus on the overall approach or the implications of the solution.

Contextual Notes

The discussion does not clarify specific assumptions or dependencies related to the constants involved, nor does it resolve any mathematical steps that may be necessary for a complete solution.

thatboi
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Hey all,
I am currently trying to solve the following equation for C:
1659137331786.png

where C is a purely imaginary value, ##F_{+}##, ##F_{-}## and ##G_{+}## and ##G_{-}## are all complex valued constants (so ##G_{+}^{*}## just means complex conjugate of ##G_{+}##. I am not really sure where to start with isolating C, any advice would be greatly appreciated!
 
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Take logarithms of both sides and see if you can solve that equation for C.
 
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Let ##F_+ /F_- = A## and ##\sqrt{ \dfrac{G_-G_+^*}{G_-^*G_+} } = B##

Your equation is ##A^{-C/2} = (-1)^{1-C}B ##

Always do simplifications and change of variables, to see what is going on.
 
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@thatboi , with the two hints given to you above, it is fairly easy to solve for C. Is that working out for you?
 
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phyzguy said:
@thatboi , with the two hints given to you above, it is fairly easy to solve for C. Is that working out for you?
Thanks for the hints I have already worked it out!
 
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Great!

May I ask where this equation came from?
 

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