Is $\mathbb Q(\pi,i\pi):\mathbb Q$ a simple extension?
$\mathbb{Q}(\pi, i\pi)$ over $\mathbb{Q}$
9
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abstract-algebra
field-theory
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0Any finite extension of $\mathbb{Q}$ is a simple extension. See the primitive element theorem. – 2011-03-16
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6@Joseph: I believe this theorem speaks about algebraic extensions, which is clearly not the case here. – 2011-03-16
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2Oops, didn't read the question closely. I'll leave the comment so others can see my shame. – 2011-03-16