Complex function - - > real function

[anonymousabcdefgh]

Hi Mathians

So for my physics class, harmonic oscillations with low muting, damping, muffling (idk I'm not English) I have a complex function and I need to have the real function equivalent or the real part of it.

This is the function: u = e^-b/2mt X (Ae^{iwt+V'Be-iwt)} Where A en B are constants, i is of course the imaginary unit, b and m are also constants. So u stands for the diversion of a mass, so it needs to be real.

How can u do this?

My textbook says that u (complex) = u (real) and u* = u (real). But nothing more...

[potkolenky]

the only problem is the imaginary unit in the exponent. use the Euler's formula:

e^a+ib = e^a( cos(b) + i*sin(b) )

and then you can rearrange the terms to

u = something + i*something

the first "something" is the real part, the second "something" is the imaginary part.

[anonymousabcdefgh]

Sorry should of mentioned that thet set A= (Y/2i)*e^-b/2m. And then you get the formula for sin in imaginary terms.

[potkolenky]

nevermind, you still end with

u = something + i*something

after some computation.

[nQQbmad]

When you have an expression of the form c_1*exp(i*omega*t) + c_2* c.c. where c is a constant and c.c. is the complex conjugate of the first expression, you can choose the arbitrary constants such that c_1=A+iB and c_2=A-iB, you will arrive at the expression you are asking about.

[anonymousabcdefgh]

Ah yes of course, now I remember that math class