Yes. Consider, if you can factor complex numbers, then logically, you should be able to take two complex numbers, multiply them together, and get a third.
That can indeed be done. For example:
(4i + 7)(3i + 2)
= -12 + 8i + 21i + 14
= 29i + 2
Therefore, the complex number 29i + 2 must be divisible by 4i + 7 and 3i + 2.
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The expression does not have any real binomial factors. x is a monomial factor, and the other two involve complex numbers.
Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.
No. Complex numbers is the highest set of numbers you can go, and there are no sets outside of complex numbers.
Real numbers are a proper subset of Complex numbers.
Complex numbers include real numbers, pure imaginary numbers, and the combination of those two.