Hi guys, What is the quickest way to find the 4 complex roots of X^4+2=0 ? I'm trying to find the splitting field for this equation over Q. Many thanks in advance. :-) x
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Originally Posted by AAM Hi guys, What is the quickest way to find the 4 complex roots of X^4+2=0 ? I'm trying to find the splitting field for this equation over Q. Many thanks in advance. :-) x $\displaystyle x^4= -2$. Write -2 in polar form- $\displaystyle -2= 2 (cos(\pi)+ i sin(\pi))$ and use DeMoivre's formula.
you can also write: $\displaystyle 0=x^4+ 2 = (x^2 + \sqrt{2})^2 - 2\sqrt{2} x^2=(x^2 + \sqrt[4]{8} x + \sqrt{2})(x^2 - \sqrt[4]{8} x + \sqrt{2}).$
Last edited by NonCommAlg; May 18th 2009 at 09:37 PM.
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