# E^(i$\omega$t) question

1. Nov 15, 2013

### 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?

2. Nov 15, 2013

### Staff: Mentor

3. Nov 15, 2013

### D H

Staff Emeritus
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.)

4. Nov 15, 2013

### 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?

5. Nov 15, 2013

### mathman

yes.

6. Nov 16, 2013

### lonewolf219

Thanks mathman

7. Nov 16, 2013

### Staff: Mentor

dont for get to thank people via the thanks button

8. Nov 17, 2013

### lonewolf219

Ok, thanks for mentioning that jedishrfu