Convert $e^{-\pi i}$ to rectangular form.
Not sure how to start this problem, should I use Euler's formula? Can anyone help provide the steps please?
Thanks
e^(-πi) = cos(-π)+ i sin(-π) = -1
Yes, you can use Euler's formula to convert $e^{-\pi i}$ to rectangular form. Euler's formula states that $e^{ix} = \cos(x) + i\sin(x)$, where $i$ is the imaginary unit.
To convert $e^{-\pi i}$ to rectangular form, we can substitute $-x$ into Euler's formula. We have:
$e^{-\pi i} = \cos(-\pi) + i\sin(-\pi)$
Now, we know that $\cos(-\pi) = -1$ and $\sin(-\pi) = 0$, so we can simplify the expression:
$e^{-\pi i} = -1 + i(0)$
The imaginary part is zero, so we are left with just $-1$ in rectangular form.
Therefore, $e^{-\pi i} = -1$.