What Does I' Represent in Zsqrt(d)?

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Homework Statement



Show I' ideal in Zsqrt(d)
Let I'=I intersection Z (where Z denotes the integers)
I any ideal in Zsqrt(d)

Homework Equations





The Attempt at a Solution


I think I' is just the set of integers in Z such that the integer is an ideal of zsqrt(d)
But how is this ideal since if I left or right multiply any element of zsqrt(d) with an element in I' I get an elementary with an imaginary component?

 
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Problem solved prof made a typo sorry
 

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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