Finding Polynomials with Integer Coefficients & \sqrt(2) + i Zero

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Homework Statement



Find a polynomial with integer coefficient for which \sqrt(2) + i is a zero.

Homework Equations



The Attempt at a Solution



I'm not sure where to really start with this one. It is on my review sheet, and I can't remember how to do it. Could someone give me a hand?
 
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duki said:

Homework Statement



Find a polynomial with integer coefficient for which \sqrt(2) + i is a zero.

Homework Equations



The Attempt at a Solution



I'm not sure where to really start with this one. It is on my review sheet, and I can't remember how to do it. Could someone give me a hand?

consider (sqrt(2)+i)2...what are you left with after expanding and simplifying?
how about (sqrt(2)+i)4?
 
Ok, as an answer I got:

x^2 - 2 \sqrt{2}x + 2 - i
Does that look right?
 
Latex isn't working, so I got

x^2 - 2sqrt(2)x + 2 - i
 

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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