How do i find the linear factors from which the polynom:
$$ x^2+i $$
Is built from.
I remember that every polynom above the complex can be represent as linear factors, but how do i do that in my example?
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Does this answer your question? What is the square root of complex number i?, resp. of $-i$. – Dietrich Burde Jun 13 '20 at 18:54
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The solution can be found also at many other places, e.g., here, or here. – Dietrich Burde Jun 13 '20 at 18:57
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Yes, thanks worked – Alon Jun 13 '20 at 19:07
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But what answered was the quora and not the link to mathstack @Dietrich Burde – Alon Jun 13 '20 at 19:08
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So have a look next time at quora, too. Just a remark, the answer here is the same as at quora. – Dietrich Burde Jun 13 '20 at 19:11
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What i meant is that he gave me a link to quora and that what helped, my question is referred to the wrong place. @Dietrich Burde – Alon Jun 13 '20 at 19:17
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No, it is not. It says "so the square roots of $i$ are $\pm\left(\frac1{\sqrt{2}}+\frac1{\sqrt{2}}i\right)$, which just gives the linear factors you want. – Dietrich Burde Jun 13 '20 at 20:25
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Ah, I see. I forgot to say that $x^2+i=(x+\sqrt{i})(x-\sqrt{i})$ by the binomial formula. Then it should be clear that it is the same. – Dietrich Burde Jun 13 '20 at 20:27