Register to reply

Complex conjugate of absolute exponential

by vg8open
Tags: complex conjugate, exponential
Share this thread:
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
Phys.Org News Partner Mathematics news on Phys.org
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
micromass
#2
Feb13-12, 09:29 PM
Mentor
micromass's Avatar
P: 18,036
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
Char. Limit's Avatar
P: 1,941
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
PF Gold
Char. Limit's Avatar
P: 1,941
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
PF Gold
Char. Limit's Avatar
P: 1,941
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.


Register to reply

Related Discussions
[complex analysis] differentiation w.r.t. complex conjugate; does it make sense? Calculus 8
How do you take this complex conjugate? General Math 4
Complex conjugate Precalculus Mathematics Homework 1
Complex conjugate Calculus & Beyond Homework 2
Complex Conjugate of Sin Precalculus Mathematics Homework 2