How to Find the Conjugate of a Complex Exponential Function?

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The discussion centers on finding the conjugate of the complex exponential function φ = exp(-x²/x₀²). It is clarified that if both x and x₀ are real, the conjugate does not change the expression, meaning φ* = φ. The participants note that the initial assumption about the conjugate being exp(x²/x₀²) is only valid if x/x₀ is imaginary. Ultimately, the conclusion is reached that since x/x₀ is real, the expression remains unchanged when taking its conjugate. The final consensus confirms that the conjugate of φ is indeed φ itself in this case.
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Homework Statement



Find the conjugate of

\varphi=exp(-x^2/x_0^2)

Homework Equations





The Attempt at a Solution




Isn't the conjugate \varphi*=exp(x^2/x_0^2)
 
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noblegas said:

Homework Statement



Find the conjugate of

\varphi=exp(-x^2/x_0^2)

Homework Equations


The Attempt at a Solution

Isn't the conjugate \varphi*=exp(x^2/x_0^2)

Not if x and x0 are real, which I suspect they are. What is it in that case?
 
Last edited:
Dick said:
Not if x and x0 are real, which I suspect they are. What is it in that case?

oh ,my solution would only be correct if x/x0 is imaginary.would my expression
<br /> exp(-x^2/x_0^2)<br /> not change when taking its conjugate??
 
noblegas said:
oh ,my solution would only be correct if x/x0 is imaginary.would my expression
<br /> exp(-x^2/x_0^2)<br /> not change when taking its conjugate??

Right, sort of. If x is imaginary the conjugate(exp(x))=exp(-x). If x is real then conjugate(exp(x))=exp(x). But your solution is only correct if (x/x0)^2 is purely imaginary.
 
Dick said:
Right, sort of. If x is imaginary the conjugate(exp(x))=exp(-x). If x is real then conjugate(exp(x))=exp(x). But your solution is only correct if (x/x0)^2 is purely imaginary.

but x/x0 is not purely imaginary , but completely real. So my expression would remain the same when taking its conjugate
 
noblegas said:
but x/x0 is not purely imaginary , but completely real. So my expression would remain the same when taking its conjugate

Yesss.
 

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