Question 987630
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12 is the only natural number.


*[tex \Large -\frac{4}{5},\ \frac{2}{7},\ 12,\ \sqrt{9},\ -5,\ \frac{1}{3}] are rational


*[tex \Large \sqrt{5}] is irrational.


Saying "the set of Imaginary numbers" is a poor way to describe things.  In fact there is only one Imaginary number and that is *[tex \Large i] which is defined as *[tex \Large i^2\ =\ -1].


Everything else someone might have told you is a member of the set of Imaginary numbers is simply *[tex \Large i] with some  real number coefficient.  The actual set is the set of Complex numbers:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \mathbb{C}\ =\ \left\{a\ +\ bi\ |\ a,b\ \in\ \mathbb{R},\ i^2\ =\ -1\right\}]


Hence, *[tex \Large 6i] is a complex number of the form *[tex \Large 0\ +\ 6i], and *[tex \Large \sqrt{-16}] is a complex number of the form *[tex \Large 0\ +\ 4i]


Note that the set of Real numbers is a subset of the Complex numbers, thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \mathbb{R}\ =\ \left\{a\ +\ bi\ \in\ \mathbb{C}\ |\ b\ =\ 0\right\}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \