Algebraic Number/Examples/Imaginary Unit

Example of Algebraic Number

The imaginary unit $i$ is an algebraic number.


Proof

We have by definition of imaginary unit that $i^2 = -1$.

Therefore $i$ is a root of $x^2 + 1 = 0$.

Hence the result by definition of algebraic number.

$\blacksquare$


Sources

  • 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $8$: Field Extensions: $\S 38$. Simple Algebraic Extensions: Example $76$
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.