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

I cannot understand how come we know this?

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- Mar 26th 2011, 10:51 AMprobladyhow 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 AMPhugoid
In a way, I've already answered this question today.

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

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

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

Hence... $\displaystyle e^{i \frac{\pi}{2}} = i $. - Mar 26th 2011, 11:06 AMproblady
Amazing!!! Thanks

- Mar 26th 2011, 03:17 PMmr fantastic