Question

Is `(sqrt(-1))x = 0` a Polynomial?

Answer 1

No.

Explanation:

Polynomials have real coefficients and non negative exponents.

`sqrt(-1)` is an imaginary number, so it is not a real coefficient.

Answer 2

By my definition it is not a polynomial.

Explanation:

In my humble opinion, the equation given is not a polynomial as it does not have more than one term. The prefix "poly" suggests more than one.

[Definition from www.mathisfun.com](https://www.mathsisfun.com/definitions/polynomial.html)
An expression that can have constants, variables and exponents, that can be combined using addition, subtraction, multiplication and division, but:
• no division by a variable.
• a variable's exponents can only be 0,1,2,3,... etc.
• it can't have an infinite number of terms.

Answer 3

Yes - it is a polynomial equation.

Explanation:

The expression `sqrt(-1)` is a constant, evaluating to the non-real complex value `i`.

So the given expression can be rewritten:

`ix = 0`

This is a linear polynomial equation.

Polynomials can have coefficients that are integers, rational numbers, irrational numbers, complex numbers, elements of rings or even semi-rings.