# how come we know that i is 90 degrees or ~1.57 rad?

• Mar 26th 2011, 10:51 AM
how come we know that i is 90 degrees or ~1.57 rad?
how come we know that i is 90 degrees or ~1.57 rad

I cannot understand how come we know this?
• Mar 26th 2011, 11:03 AM
Phugoid
In a way, I've already answered this question today.

But, in general, when we multiply something by $e^{i\theta}$, we rotate it through an angle $\theta$ in the complex plane.

Now, if we want to rotate something by $90^o$, we would multiply it by $e^{i\frac{\pi}{2}}$.

Now, if you remember that $e^{i\theta} = \cos(\theta) + i \sin(\theta)$, and that $\cos(\frac{\pi}{2}) = 0$ and $\sin(\frac{\pi}{2}) = 1$.

Hence... $e^{i \frac{\pi}{2}} = i$.
• Mar 26th 2011, 11:06 AM
Amazing!!! Thanks
• Mar 26th 2011, 03:17 PM
mr fantastic
Quote:

Originally Posted by problady
how come we know that i is 90 degrees or ~1.57 rad

I cannot understand how come we know this?

Review the definition of a radian.