Imaginary Numbers Rational Or Irrational. Of course all real numbers are either rational or irrational numbers. 2 it turns out that most other roots are also irrational.
The complex number system is an extension of the real number system just as the real number system is an extension of the rational numbers numbers of the form of a ratio of two integers. If the number line is expanded to become a number plane some numbers that are neither. 3 times the square root of 11 2.
This is similar to how it makes no sense to ask if 1 3 is even.
No but rational and irrational only apply to real numbers so it doesn t even make sense to ask if a complex number rational or irrational. Imaginary numbers are discussed in chapter 15 of this course. Real numbers are either rational or irrational. The complex number system is an extension of the real number system just as the real number system is an extension of the rational numbers numbers of the form of a ratio of two integers.