Eulers formula - Complex math

[gusrohar]

Hi, I am stuck on a problem where I have to give a plausible value to cos i.
The answer is cos i = (1+e^2)/2e but I have a bit of a problem getting there and I was wondering if anybody could solve so that I could follow the steps.

Thanks!

 

[Deleted member 4993]

Hi, I am stuck on a problem where I have to give a plausible value to cos i.
The answer is cos i = (1+e^2)/2e but I have a bit of a problem getting there and I was wondering if anybody could solve so that I could follow the steps.

Thanks!

Use Euler's (corollary of) equation:

\(\displaystyle \displaystyle \cos(\theta) \ = \ \dfrac{e^{i\theta} \ + \ e^{-i\theta}}{2}\)

Now replace \(\displaystyle \theta\) by i.

 

[gusrohar]

Use Euler's (corollary of) equation:

\(\displaystyle \displaystyle \cos(\theta) \ = \ \dfrac{e^{i\theta} \ + \ e^{-i\theta}}{2}\)

Now replace \(\displaystyle \theta\) by i.

I knew it was going to be an answer that was obvious yet somehow seemingly impossible to solve. Thank you!