7
votes
1answer
280 views

Is every complex number the root of a polynomial? (Converse to fundamental theorem of algebra.)

For every polynomial with complex coefficients, the fundamental theorem of algebra guarantees the existence of complex numbers which happen to be roots of it. But is this everything? i.e. is the ...
1
vote
1answer
187 views

Are numbers : $(-1)^{i} , 1^{-i} , 1^{i} $ transcendental numbers? [duplicate]

Possible Duplicate: What is the value of 1^i? According to Euler's formula : $e^{ix}=\cos x + i\cdot \sin x$ we may write : $$e^{i\cdot \frac{\pi}{2}}=i \Rightarrow \left(e^{i\cdot ...