# Math Help - squaring exponentials

1. ## squaring exponentials

is $(e^(i \theta))(e^(i \theta))$ = $e^(2i \theta))$

2. 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:

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

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

is $(e^{i \theta})(e^{i \theta})$ = $e^{2i \theta})$
$$e^{2i \theta}$$ gives $e^{2i \theta}$.