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What is a polynomial that does not factor over the real numbers referred to as?
There is no specific term for such polynomials. They may be referred to as are polynomials with only purely complex roots.
What is complex math?
Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.
What happens when you square root a negative number?
The square root of a negative number is not real. However, there is a field of numbers known as the complex number field which contains the reals and in which negative numbers have square roots. Complex numbers can all be expressed in the form a+bi where a and b are real and i is the pure imaginary such that i2=1. Please see the related links for more information about complex and imaginary numbers.
What is the significance of complex roots?
One significant feature of complex numbers is that all polynomial equations of order n, in the complex field, have n solutions. When multiple roots are Given any set of complex numbers {a(0),  … , a(n)}, such that at least one of a(1) to a(n) is non-zero, the equation a(n)*z^n + a(n-1)*z^(n-1) + ... + a(0) has at least one solution in the complex field. This is the Fundamental Theorem of Algebra and establishes the set of Complex numbers as a closed field. [a(0), ... , a(n) should be written with suffices but this browser has decided not to be cooperative!] The above solution is the complex root of the equation. In fact, if the equation is of order n, that is, if the coefficient a(n) is non-zero then, taking account of the multiplicity, the equation has exactly n roots (some of which may be real).
When were imaginary numbers developed?
Imaginary numbers were first recognised in the first century CE by Heron of Alexandria but development was slow because "the establishment" did not consider these to be proper numbers. Gerolamo Cardano, in his work on finding roots of cubic equations in early 16th century CE, set out some of the rules for manipulating complex numbers. Rafael Bombelli set down the rules for multiplication of complex numbers later in that century. However there was no serious work done on these numbers for a long time: their name did not help. It was not until two of the giants of mathematics, Leonhard Euler and Carl Friedrich Gauss in the 18th century worked on them that they were accepted as worthy of attention by serious mathematicians! And the rest, as they say, is history!
What are the compex roots in mathematics?
The complex roots of an equation is any solution to that equation which cannot be expressed in terms of real numbers. For example, the equation 0 = x² + 5 does not have any solution in real numbers. But in complex numbers, it has solutions.
How do you find the square root of negative numbers?
For most school mathematics, negative numbers do not have square roots. This is because a negative number multiplied by itself is a negative times a negative and so is positive. When (if) you study advanced mathematics, you will learn that there is a solution and this falls within the realms of complex mathematics and imaginary numbers.
What are complex root?
The complex roots of an equation are the complex numbers that are solutions to the equation.
Where you use complex number?
Complex numbers are the square roots of negative numbers. i.e. root -1 = i
How do you simplify fourth roots?
The answer will depend on the form of the fourth root. Positive real numbers will have two fourth roots which are real and two that are complex. Complex numbers will have four complex roots. However, none of these can be "simplified" in the normal sense of the term.
What are positive square roots called?
They are called real numbers. Negative square roots must be complex numbers.
How many types of numbers are there in mathematics?
Natural numbers Integers Rational numbers Real numbers Complex numbers
What is equivalent to square root -80?
A negative number cannot have a square root in basic mathematics. However, in more advanced mathematics, you will study complex numbers. And there you will find that the square roots of -80 are ± 8.944*i where i is the imaginary square root of -1.Incidentally, ± 8.944 are the square roots of +80.
What do you think is true of the square roots of a complex number?
I posted an answer about cube roots of complex numbers. The same info can be applied to square roots. (see related links)
Why are there two integer answers for square roots but only one integer answer for cubed roots?
When (if) you learn more advanced mathematics you will find that there are, in fact 3 cube roots for any non-zero number (in the complex field). In general, there are n nth roots (de Moivre's theorem). However, only one of the cube roots can be a real number, the other two are complex numbers. The reason is that the product of a pair of negative numbers is positive. As a result both x and -x are square roots of x^2. But the product of three negative numbers is itself negative, so for cube roots the signs match up.
Why do principal roots of negative numbers have to be different in real numbers or complex numbers?
Because in real numbers they are not defined.
What the square roots of -256?
There are no real square roots of -256. But using complex numbers the square roots of -256 are 16i and -16i.
