E^(i[itex]\omega[/itex]t) question

[lonewolf219]

x(t)=e^(i$\omega$t)

Is this the correct notation to define this function?

f:C$\rightarrow$R

Does this exponential function take a complex element from the set C and assign to it a real element from the set R?

 

[jedishrfu]

The x(t) function is known as Euler's equation: e^ix = cos(x) + i*sin(x)

http://en.wikipedia.org/wiki/Euler's_formula

so based on that I'd say no it doesn't map complex to real.

 

[D H]

It's the other way around assuming that ω and t are real. $f(\omega,t) = e^{i\omega t}$ maps ℝ×ℝ to ℂ. (Specifically, to the complex unit circle rather than ℂ in general.)

 

[lonewolf219]

Thanks for the replies! D H, is the complex unit circle in the complex plane, meaning that the x-axis is the real number line and the y-axis is the imaginary number line?

 

[mathman]

Thanks for the replies! D H, is the complex unit circle in the complex plane, meaning that the x-axis is the real number line and the y-axis is the imaginary number line?

yes.

 

[lonewolf219]

Thanks mathman

 

[jedishrfu]

dont for get to thank people via the thanks button

 

[lonewolf219]

Ok, thanks for mentioning that jedishrfu