Scientific name of square root of negative number

Question

How do you call a number in the form:

$\sqrt{-4}$ ?

A non real number?

Answer 1

It is $$1)\,\,\text{complex,}$$ (all reals like $2$, $-\pi$ and $\sqrt5+1$ are complex) $$2)\,\,\text{non-real}$$ (which is, probably, what are you interested in) and $$3)\,\,\text{purely imaginary}$$ (which, you may say, is a coincidence: although all square roots of negative reals are purely imaginary, complex numbers include both real and purely imaginary numbers, but there are also infinitely many other complex numbers which are non-real and non-purely imaginary).

If this does not address your issue or you expect further clarification, please communicate via the comments section.

Answer 2

"Complex number" is frequently used. And sometimes they are called "imaginary numbers".

Answer 3

I call out " two ei!" when is pure imaginary.

For complex $ (2+ 3 i) $ I call out " two plus three ei.. complex!"

Answer 4

In the 9th century, those expressions would have no name, because "they did not exist" (see the notice on Mahavira).

Imaginery number once was a generic derogatory name for those ficticious or useless quantities. L. Euler used (in Elements of Algebra) also used impossible numbers.

Now those quantities are accepted, a negative number admits two square roots, here $2i$ and $-2i$, whose real part is null. They are often called pure imaginary numbers. As such, it is also a complex number.

But it is a solution of an algebraic equation ($x^2+4=0$), so it is also an algebraic number. And a Gauss integer as well, as it real and imaginary parts are integers. Yet, it is also a (model of) a quaternion, of an octonion, etc. There is a lot of interpretations of a quantity, and it really depends on you knnowledge and your goal.

A little history of complex numbers could be an interesting reading.