I Simplify Tricky Equation for Purely Imaginary C with Complex Constants

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The discussion revolves around solving an equation for a purely imaginary value C, where F and G are complex constants. Participants suggest taking logarithms and simplifying the equation by introducing variables A and B. It is noted that with the provided hints, isolating C becomes straightforward. The original poster confirms they successfully solved the equation after receiving guidance. The conversation ends with a request for the origin of the equation.
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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