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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)
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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 the Multiplicative Identity for rational numbers?
It is 1, as it is for all complex numbers - which includes real numbers.
What are inverse numbers?
An inverse, without any qualification, is taken to be the multiplicative inverse. is The inverse of a number, x (x not 0), is 1 divided by x. Any number multiplied by its inverse must be equal to 1. There is also an additive inverse. For any number y, the additive inverse is -y. And the sum of the two must always be 0.
How do you write a program to print Inverse number in PHP?
There are two types of inverse numbers in this context: additive and multiplicative. An additive inverse number is a number that's had its sign flipped: positive becomes negative, and negative becomes positive. The PHP code for this would be: $result=-$number; A multiplicative inverse number is a number that's been divided into 1. So 5 becomes 1/5, and 1/5 becomes 1/1/5, or 5. The PHP code for this would be: $result=1/$number;
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.
