Generate Quiz 6A1D7CFAD55D8

The closure property with regard to addition (+) is the property that is shown. According to the closure property, an operation defined on a set will produce another element in the same set if it is performed on any two elements in the set. Put more simply, two real numbers added together will likewise result in a real number. In mathematics, (a + b) is a real number if a and b are real numbers.

Any number that can be represented as a fraction with an integer (whole number) in the numerator and a non-zero denominator is considered rational. Any number that cannot be represented in this manner as a fraction is considered irrational.

The decimal 0.1428571428571… repeats. A fraction can always be used to express this type of decimal representation.

Let us take the repeating decimal 0.5555, for instance.

We can allow this decimal to be equal to x. After that, we obtain the following by multiplying both sides of the equation by 10:

10x = 5.5555…

The result of subtracting the two equations is:

9 times is 5.

x = 5/9

Thus, the rational number 5/9 can be represented as 0.5555…

By using the same reasoning, we can determine that 0.1428571428571… is a rational number by expressing it as a fraction.

The number you multiply by to obtain 1 is known as the multiplicative inverse of a number, or its reciprocal. For instance, since 5 x (1/5) = 1, the multiplicative inverse of 5 is 1/5. You can’t divide by zero, though. Therefore, multiplying any number by zero will yield zero, and there isn’t a single number that can be multiplied by zero to obtain 1. Consequently, there is no definition for the multiplicative inverse of 0.

This is a fundamental characteristic of numbers. All numbers are equal to one another.

z + z̄ = x + ίy + x – ίy

= 2x

= 2 real parts of z

= 2 Re (z)

(b) Commutative property with respect to + is the right choice. According to the commutative property, the order in which numbers are added has no bearing on the total. Stated differently, a + b equals b + a. This property is demonstrated by the following statement: a + b = b + a.

The imaginary unit, denoted by the variable i, is the square root of -1. Stated differently, i = √-1.

An odd number will always be an odd number when it is raised to any power, including another odd number.

Consequently, i will remain i even though n (which is odd) is being raised to an unknown odd power because:

in = (√-1)n = √(-1)n = -1 (if n is odd)