One
Every non zero number has a multiplicative inverse, which is 1 divided by that number. This stands for both real and complex numbers. This can be proved by letting x=some non zero number. x*(1/x)=x/x=1, therefore the multiplicative inverse of x is 1/x.
change it to an improper fraction and then do it
1
The multiplicative inverse of 4i is -(1/4)*i.
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.
A multiplicative inverse for 2 numbers exists if the 2 numbers are coprime, i.e. their greatest common divisor (or gcd) is 1. However, if your question refers to just a singular number, virtually all real numbers (with the exception of zero) have a multiplicative inverse.
The inverse function of multiplication is division.
One
The only real (or complex) number which does not have a multiplicative inverse is 0. There is nothing you can multiply by 0 to get 1.
On the set of all real numbers ZERO has no multiplicative inverse. For other sets there may be other numbers too, so please define your set!
Yes, and for any non-zero rational x, the multiplicative inverse is 1/x.
Assuming the question is about the multiplicative inverse, the answer is, -1. It is its own multiplicative inverse.
Yes. That's basically the definition of a multiplicative inverse.Also, this doesn't only apply to fractions - it applies to any real numbers.
No, it is not true.
Every non zero number has a multiplicative inverse, which is 1 divided by that number. This stands for both real and complex numbers. This can be proved by letting x=some non zero number. x*(1/x)=x/x=1, therefore the multiplicative inverse of x is 1/x.
change it to an improper fraction and then do it