How to Find the Conjugate of a Complex Exponential Function?

[noblegas]

Homework Statement

Find the conjugate of

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

Homework Equations

The Attempt at a Solution

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

 

[Dick]

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?

 

[noblegas]

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
$$exp(-x^2/x_0^2)$$ not change when taking its conjugate??

 

[Dick]

oh ,my solution would only be correct if x/x0 is imaginary.would my expression
$$exp(-x^2/x_0^2)$$ 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.

 

[noblegas]

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

 

[Dick]

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

Yesss.