Are all rational numbers complex numbers?

Are all imaginary numbers irrational?

√2 is irrational. Just like rational numbers have repeating decimal expansions (or finite ones), the irrational numbers have no repeating pattern. Together, the irrational and rational numbers are called the real numbers which are often written as . These are all numbers we can see along the number line.

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers. Mathematicians do not generally take “terminating or repeating” to be the definition of the concept of rational number.

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. Because no real number satisfies this equation, i is called an imaginary number.

In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, and its square is −25. Zero is considered to be both real and imaginary.

Essentially, an imaginary number is the square root of a negative number and does not have a tangible value. While it is not a real number — that is, it cannot be quantified on the number line — imaginary numbers are “real” in the sense that they exist and are used in math.

The ordering of Z is given by: :… −3 < −2 < −1 < 0 < 1 < 2 < 3 < … An integer is positive if it is greater than zero and negative if it is less than zero. Zero is defined as neither negative nor positive.

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356, the square root of 2, an irrational algebraic number).

Irrational, then, just means all the numbers that aren’t rational. Every integer is a rational number, since each integer n can be written in the form n/1. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point. Here are some irrational numbers: π = 3.141592…

4 Answers. Every real number is a complex number. Therefore , which is a real number, is a complex number. is not an imaginary number, which are numbers in the form of , x ∈ R .

Normally I have always taken the Natural Numbers to start at 1 and not to include zero. Natural Numbers are 1,2,3,4,5, [] and Whole numbers are 0,1,2,3, According to Wikipedia: In mathematics, a natural number is either a positive integer (1, 2, 3, 4, ) or a non-negative integer (0, 1, 2, 3, 4, ).

In number theory, two integers a and b are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1. This is equivalent to their greatest common divisor (gcd) being 1.

A non-real, or imaginary, number is any number that, when multiplied by itself, produces a negative number. Mathematicians use the letter “i” to symbolize the square root of -1. An imaginary number is any real number multiplied by i. For example, 5i is imaginary; the square of 5i is -25.

Integers. The integers are , -4, -3, -2, -1, 0, 1, 2, 3, 4, — all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero). Fractions and decimals are not integers. For example, -5 is an integer but not a whole number or a natural number.

A complex number is said to be purely imaginary if it has no real part, i.e., . The term is often used in preference to the simpler “imaginary” in situations where can in general assume complex values with nonzero real parts, but in a particular case of interest, the real part is identically zero.

The rational numbers includes all positive numbers, negative numbers and zero that can be written as a ratio (fraction) of one number over another. Whole numbers, integers, fractions, terminating decimals and repeating decimals are all rational numbers.

So imaginary numbers aren’t integers. There are other numbers that act a lot like integers, and they can be called integers if you toss in an adjective making it clear that you’re not talking about the usual integers. Gaussian integers are complex numbers of the form m + n i where both and are ordinary integers.

Natural numbers are the set of positive integers, that is, integers from 1 to ∞ excluding fractional n decimal part. They are whole numbers excluding zero.Natural Numbers are also called counting numbers. Zero is the only whole number which is not a natural number.

Mathwords: Real Numbers. All numbers on the number line. This includes (but is not limited to) positives and negatives, integers and rational numbers, square roots, cube roots , π (pi), etc. Real numbers are indicated by either or .

Rational solutions. Often the solutions to quadratic equations are rational numbers, which are integers or fractions. The requirement for the solution to be an integer or fraction is that √(b2 − 4ac) is a whole number.