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

**problady** · March 26th 2011, 10:51 AM

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

I cannot understand how come we know this?

**Phugoid** · March 26th 2011, 11:03 AM

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... $e^{i \frac{\pi}{2}} = i$ .

**problady** · March 26th 2011, 11:06 AM

Amazing!!! Thanks

**mr fantastic** · March 26th 2011, 03:17 PM

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.

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