# Exponential Form Question

1. Sep 2, 2009

### DEMJ

1. The problem statement, all variables and given/known data
Show that

$$\overline{e^{i\theta}} = e^{-i\theta}$$

2. Relevant equations

3. The attempt at a solution

So I what's going through my mind is that the problem above is pretty much the same as saying $$\bar{z} = z^{-1}$$

Then to prove it is all I need to say is that since $$\overline{e^{i\theta}} = (cos\theta - isin\theta)$$ and $$e^{-i\theta} = (cos\theta - isin\theta)$$

so then they are equal. Is this sufficient or am I totally under thinking it?

2. Sep 2, 2009

### aPhilosopher

equal is equal. That's a silly problem. maybe show that bar above $$cos \theta + i sin \theta$$ just to be on the safe side.

3. Sep 2, 2009

### rock.freak667

Well that is how I would do it.

4. Sep 2, 2009

### aPhilosopher

ignore my last post, do $$e^{-i\theta} = cos( -\theta) + i sin (-\theta)$$ and take it from there.

The reason being that you want to apply any factors in the exponent to $$\theta$$ rather than to i.

5. Sep 2, 2009

### NJunJie

my opinion is to use trigonometry to prove exp functions and try to use reverse; i.e exp functions to prove trigonometry in complex analysis. thats my suggestions.
esp. Euler formula

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