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You can invert almost any number by dividing 1 by that number. Zero is an exception since division by zero yields the equivalent of infinity, which is difficult to deal with by the usual rules of arithmetic. We cannot really know what the product of zero and infinity is. All other real numbers can be inverted.
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DevinNo, zero does not. Multiplicative inverse, also known as reciprocal, is a number which multiplied by the original number gives 1 for the answer. Zero, multiplied by any numberequals zero. Infinity is not an actual number that you can multiply by. These are important concepts.
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What are the elements in rational numbers having multiplicative inverse?
All rational numbers, with the exception of zero (0), have a multiplicative inverse. In fact, all real numbers (again, except for zero) have multiplicative inverses, though the inverses of irrational numbers are themselves irrational. Even imaginary numbers have multiplicative inverses (the multiplicative inverse of 5i is -0.2i - as you can see the inverse itself is also imaginary). Even complex numbers (the sum of an imaginary number and a real number) have multiplicative inverses (the inverse of [5i + 2] is [-5i/29 + 2/29] - similar to irrational and imaginary numbers, the inverse of a complex number is itself complex). The onlynumber, in any set of numbers, that does not have a multiplicative inverse is zero.
What is a multiplicative inverse of an imaginary number?
The same as for a real number: 1 divided by the number.For example, the multiplicative inverse (or reciprocal) of 2i is 1 / 2i = -(1/2)i.
Which of the following sets of numbers contains multiplicative inverses for all its elements Positive Integers Integers Rational Numbers Real Numbers?
Rational numbers and Real Numbers. The multiplicative inverses of integers are not integers.
What is the Multiplicative inverse formula of complex numbers?
So if you have a number z = a + bi. Then how to find 1 divided by z. The way to figure this is to get the denominator as a pure real number. Multiplying the numerator and the denominator by the complex conjugate {a - bi} will result in a pure real denominator.(a - bi)(a + bi) = a² + abi - abi - (bi)² = a² + b². So the multiplicative inverse is(a - bi)/(a² + b²)
What is the Multiplicative Identity for rational numbers?
It is 1, as it is for all complex numbers - which includes real numbers.
