Complex conjugate of absolute exponential

[vg8open]

Hello all,

I am trying to figure out how to solve for the complex conjugate of the following: (-0.5)^abs(x)

Thanks for your help.

-Brian

 

[micromass]

What is the definition of complex conjugation?? Try to apply that first on your expression.

 

[SteveL27]

Hello all,

I am trying to figure out how to solve for the complex conjugate of the following: (-0.5)^abs(x)

Thanks for your help.

-Brian

abs(x), usually denoted |x|, is a nonnegative real number whether x is real or complex.

So your expression is real. Which makes its conjugate very easy to compute!

 

[Char. Limit]

abs(x), usually denoted |x|, is a nonnegative real number whether x is real or complex.

So your expression is real. Which makes its conjugate very easy to compute!

Not necessarily. What if x=1/4?

 

[SteveL27]

Not necessarily. What if x=1/4?

Oops missed the minus sign. Thanks.

 

[Char. Limit]

Hello all,

I am trying to figure out how to solve for the complex conjugate of the following: (-0.5)^abs(x)

Thanks for your help.

-Brian

It's a whole lot easier if you put it into complex exponential, or even better, cos + i sin notation.

 

[vg8open]

It's a whole lot easier if you put it into complex exponential, or even better, cos + i sin notation.

I think I missing something here... Are you talking about these equations?
$$a^b = e^{(\ln(r) + \phi i)b}$$ and $$e^{ix} = \cos(x) +i\sin(x)$$

 

[Char. Limit]

Well, by complex exponential, I just mean putting it into r e^(i theta) for some theta and r. But the cos + i sin notation I was talking about, yeah, you got it.