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
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.