Understanding I^(-i) and How to Solve for It

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Really struggling with this question on my homework, can anybody help out? According to google the answer is 4.81047738 but I need to know how to get there.

Thanks for your help,
Pete.
 
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Can you rewrite i in polar form using Euler's equation?
 
e^(i.pi/2)?

I feel I'm getting close with some work I've done on paper.
 
You're done. Now put that in for i (the base).
 
Excellent, I've got it.

Thanks for your help neutrino
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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