# squaring exponentials

• Mar 24th 2011, 01:04 PM
squaring exponentials
is $(e^(i \theta))(e^(i \theta))$ = $e^(2i \theta))$
• Mar 24th 2011, 01:18 PM
Yes, it is true. You have the two formulae:

$e^{i\theta}=cos(\theta)+isin(\theta)$

For $2\theta$

$e^{i(2\theta)}=cos(2\theta)+isin(2\theta)$

You can show that your equation is true as follows:

$(e^{i\theta})(e^{i\theta})$

$=\left[cos(\theta)+isin(\theta)\right]\left[cos(\theta)+isin(\theta)\right]$

$=cos^2(\theta)+2isin(\theta)cos(\theta)+i^2sin^2(\ theta)$

Remember:

$i^2=-1$

So the equation simplifies to:

$=cos(2\theta)+isin(2\theta)$

$=e^{i(2\theta)}$
• Mar 24th 2011, 01:25 PM
Plato
Quote:

Originally Posted by adam_leeds
is $(e^{i \theta})(e^{i \theta})$ = $e^{2i \theta})$

Yes it is.

BTW. See how I fixed the exponents is the LaTeX.
$$e^{2i \theta}$$ gives $e^{2i \theta}$.
Note the braces about the exponents with more that one character.