Algebraic Number/Examples/Imaginary Unit
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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 $76$