Complex number and split complex number

[brunotolentin.4]

Is correct to afirm that a solution of a quadratic equation or is a complex number or is a split complex number?

 

[jedishrfu]

Solutions to quadratic equations are either real values or complex values:

https://en.wikipedia.org/wiki/Quadratic_equation

https://en.wikipedia.org/wiki/Complex_number

Split-complex numbers are a whole different other animal:

https://en.wikipedia.org/wiki/Split-complex_number

@HallsofIvy or @Mark44 might be able to provide a better answer.

 

[HallsofIvy]

A quadratic equation may have a double root or two distinct roots. Assuming you mean a quadratic equation with real coefficients then if the equation has a double root, it must be real. If there are two distinct roots they must be complex conjugates. I don't know what you mean by a "split complex number". Here, I am using the term "complex number" in the general sense, including the real numbers as a subset of the complex numbers.

 

[pbuk]

If there are two distinct roots they must be complex conjugates.

I think you mean if there are two distinct roots they must either both be real or be complex conjugates.

Split complex numbers have nothing to do with quadratic equations and, in contrast with complex numbers which feature in many areas of maths and physics, split complex numbers are encountered in a few advanced and specialised areas.