# Complex conjugate of absolute exponential

1. Feb 13, 2012

### 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

2. Feb 13, 2012

### micromass

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

3. Feb 13, 2012

### SteveL27

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!

4. Feb 13, 2012

### Char. Limit

Not necessarily. What if x=1/4?

5. Feb 14, 2012

### SteveL27

Oops missed the minus sign. Thanks.

6. Feb 14, 2012

### Char. Limit

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

7. Feb 14, 2012

### vg8open

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

8. Feb 14, 2012

### 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.