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What are imaginary numbers? - Mathematics Stack Exchange $\begingroup$ +1 but you didn't complete the definition that the imaginary number line as simply the axis orthogonal to the real number line in the complex number plane so that every complex number can be expressed as the sum of a real number and an imaginary number $\endgroup$ –
Whats the precise meaning of imaginary number? Let me address your first question about "what's the precise meaning of imaginary number? First though, in my opinion, we have to be careful when we start to give meaning to mathematical objects When we talk about "meaning" then the answer, IMO, becomes subjective and so to ask for the precise meaning doesn't really make sense
notation - What is the symbol for imaginary numbers? - Mathematics . . . [Fun Trivia Fact: $0$ is an imaginary number $0$ is a real number $0$ is the only real number that is imaginary and the only imaginary number that is real ] Also notice: Despite all the fan fare about learning that Imaginary Numbers exist, they actually aren't in the least bit interesting or important
Is 0 a real and imaginary number? - Physics Forums "In mathematics, an imaginary number (or purely imaginary number) is a complex number whose squared value is a real number not greater than zero" As zero squared is zero, it fits the definition here too I saw another definition: "An imaginary number is a quantity of the form ix, where x is a real number and i is the positive square root of -1"
Is infinity an imaginary number? - Physics Forums Is it imaginary? No Imaginary numbers are well defined and do not include a number called infinity Is it real? No, the real numbers are also well defined and do not include infinity But no number is "real" in a philosophical sense, they are concepts In the natural number system rationals do not exist
Is 0 a Real Number, an Imaginary Number, or Both? - Physics Forums Anyway, to actually answer the question of the OP Yes, 000 is a real number Yes, 000 is a complex number Whether 000 is an imaginary number is a bit difficult though since there are various definitions for imaginary numbers One defines imaginary numbers as being of the form bibibi with b≠0b≠0b\neq 0, others do allow b=0b=0b=0
Why is $1 i$ equal to $-i$? - Mathematics Stack Exchange There are multiple ways of writing out a given complex number, or a number in general Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot cleaner than saying $1-1$ for example The complex numbers are a field This means that every non-$0$ element has a multiplicative inverse, and that inverse is unique
What is the norm of a complex number? [duplicate] $\begingroup$ To add a tiny bit of clarity to the excellent answers below: if you are told in the first place that z is an algebraic number, then it must reside in some finite extension K of the rational numbers
How do you integrate imaginary numbers? - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers