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Complex conjugate of absolute exponential

by vg8open
Tags: complex conjugate, exponential
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vg8open
#1
Feb13-12, 08:23 PM
P: 2
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
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micromass
#2
Feb13-12, 09:29 PM
Mentor
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What is the definition of complex conjugation?? Try to apply that first on your expression.
SteveL27
#3
Feb13-12, 09:48 PM
P: 800
Quote Quote by vg8open View Post
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
#4
Feb13-12, 09:52 PM
PF Gold
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P: 1,951
Complex conjugate of absolute exponential

Quote Quote by SteveL27 View Post
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
#5
Feb14-12, 01:39 PM
P: 800
Quote Quote by Char. Limit View Post
Not necessarily. What if x=1/4?
Oops missed the minus sign. Thanks.
Char. Limit
#6
Feb14-12, 01:54 PM
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Quote Quote by vg8open View Post
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
#7
Feb14-12, 06:11 PM
P: 2
Quote Quote by Char. Limit View Post
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?
[tex] a^b = e^{(\ln(r) + \phi i)b} [/tex] and [tex]e^{ix} = \cos(x) +i\sin(x) [/tex]
Char. Limit
#8
Feb14-12, 06:12 PM
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P: 1,951
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.


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