Algebraic Number/Examples
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Examples of Algebraic Numbers
The algebraic numbers include the following:
Rational Number is Algebraic
Let $r \in \Q$ be a rational number.
Then $r$ is also an algebraic number.
$\sqrt 2$ is Algebraic
- $\sqrt 2$ is an algebraic number.
$\sqrt {2 + \sqrt 3}$ is Algebraic
- $\sqrt {2 + \sqrt 3}$ is an algebraic number.
$\sqrt [3] {2 + \sqrt 2}$ is Algebraic
- $\sqrt [3] {2 + \sqrt 2}$ is an algebraic number.
$\sqrt [3] 2 + \sqrt 3$ is Algebraic
- $\sqrt [3] 2 + \sqrt 3$ is an algebraic number.
$\sqrt 3 + \sqrt 2$ is Algebraic
- $\sqrt 3 + \sqrt 2$ is an algebraic number.
$2 - \sqrt 2 i$ is Algebraic
- $2 - \sqrt 2 i$ is an algebraic number.
$\sqrt [3] 4 - 2 i$ is Algebraic
- $\sqrt [3] 4 - 2 i$ is an algebraic number.
Golden Mean is Algebraic
- The golden mean $\phi = \dfrac {1 + \sqrt 5} 2$ is an algebraic number.
Imaginary Unit is Algebraic
- The imaginary unit $i$ is an algebraic number.
$-7$ is Algebraic
- $-7$ is an algebraic number.
$\frac 5 2$ is Algebraic
- $\dfrac 5 2$ is an algebraic number.
$3 - i$ is Algebraic
- $3 - i$ is an algebraic number.
$\sqrt [3] 6$ is Algebraic
- $\sqrt [3] 6$ is an algebraic number.
$\frac 1 3 \paren {1 + i \sqrt 2}$ is Algebraic
- $\dfrac 1 3 \paren {1 + i \sqrt 2}$ is an algebraic number.