Additive Inverse Calculator
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For example, the additive inverse of 7 is âˆ’7, because 7 + (âˆ’7) = 0, and the additive inverse of âˆ’0.3 is 0.3, because âˆ’0.3 + 0.3 = 0.
In other words, the additive inverse of a number is the number's negative. For example, the additive inverse of 8 is −8, the additive inverse of 10002 is −10002 and the additive inverse of xÂ² is −(xÂ²).
Integers, rational numbers, real numbers, and complex number all have additive inverses, as they contain negative as well as positive numbers. Natural numbers, cardinal numbers, and ordinal numbers, on the other hand, do not have additive inverses within their respective sets. Thus, for example, we can say that natural numbers do have additive inverses, but because these additive inverses are not themselves natural numbers, the set of natural numbers is not closed under taking additive inverses.
The notation '+' is reserved for commutative binary operations, i.e. such that x + y = y + x, for all x,y. If such an operation admits an identity elemento (such that x + o (= o + x) = x for all x), then this element is unique (o' = o' + o = o). If then, for a given x, there exists x' such that x + x' (= x' + x) = o, then x' is called an additive inverse of x.
If '+' is associative ((x+y)+z = x+(y+z) for all x,y,z), then an additive inverse is unique
- ( x" = x" + o = x" + (x + x') = (x" + x) + x' = o + x' = x' )
â€“ y instead of x + (â€“y).
For example, since addition of real numbers is associative, each real number has a unique additive inverse.
All the following examples are in fact abelian groups:
- addition of real valued functions: here, the additive inverse of a function f is the function â€“f defined by (â€“ f)(x) = â€“ f(x), for all x, such that f + (â€“f) = o, the zero function (o(x) = 0 for all x).
- more generally, what precedes applies to all functions with values in an abelian group ('zero' meaning then the identity element of this group):
- * complex valued functions,
- * vector space valued functions (not necessarily linear),
- sequences, matrices and nets are also special kinds of functions.
- In a vector space additive inversion corresponds to scalar multiplication by âˆ’1. For Euclidean space, it is inversion in the origin.
- In modular arithmetic, the modular additive inverse of x is also defined: it is the number a such that a+x â‰¡ 0 (mod n). This additive inverse does always exist. For example, the inverse of 3 modulo 11 is 8 because it is the solution to 3+x â‰¡ 0 (mod 11).
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Answers:additive inverse of any number 'a' simply means a number 'b' such that a+b=0, that is b = -a So, if the complex number is 'p + iq', its additive inverse is: - p - iq If you need to know abt multiplicative inverse, google on it, i am attaching a good link i know.
Answers:An additive inverse is the number when added will equal zero, thus -3 is the additive inverse of 3, and 3 is the additive inverse of -3. Best of luck! :)
Answers:1. Zero; that is the definition of additive inverse. For any number x, the additive number of x is -x, so that x + (-x) = 0. 2. One; that is the definition of multiplicative inverse. For any number x, the multiplicative inverse of x is 1/x, so that (x)(1/x)= 1.
Answers:Well, go back to the definition: What do you add to 2.5 to get zero? x + 2.5 = 0 What do you multiply by to get one? x * 2.5 = 1 Solve those, and there's your first pair of answers. Do the same for the second one. If you have a calculator, there's an even easier way: the +/- button does additive inverse; the 1/x button does multiplicative inverse.