# How to reciprocal this imaginary exponent?

Assume $x\gt 0$, how does one simplify $$e^{(-x^2t)/i}\ ?$$

I don't understand how we could change the i under to the top so I could use Euler's formula

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$\,\frac{1}{i}=-i\,$...of course, assuming you're talking of the imaghinary unit. – DonAntonio Jul 2 '12 at 22:15
Since $\frac{1}{i} = -i$, your expression is equal to $e^{ix^2t}$ – Joel Cohen Jul 2 '12 at 22:15
Damn it, and I just figured it out myself lol. Which is funny because I spent 20 minutes whether I should ask this or not and then comes up with a solution immediately I asked – Hawk Jul 2 '12 at 22:16

Remember that $-i^2 = 1$ implies that $-i = \frac{1}{i}.$ Then apply Euler's formula as you mention.
$\frac{1}{i}=-i$. In general, $\frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}$. You can probably figure out the rest.