# Are complex numbers real numbers?

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 x^{2}= −1. Because no**real number**satisfies this equation, i is called an**imaginary number**.A.

### Is an imaginary number a complex 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 i^{2}= −1. The square of an**imaginary number**bi is −b^{2}. For example, 5i**is an imaginary number**, and its square is −25.#### Is a complex number?

A**complex number**is a**number**of the form a + bi, where a and b are real**numbers**and i is an indeterminate satisfying i^{2}= −1. For example, 2 + 3i**is a complex number**.#### Are all complex numbers are real numbers?

Either Part Can Be Zero. So, a**Complex**Number has a**real**part and an imaginary part. But either part can be 0, so**all Real Numbers**and Imaginary**Numbers**are also**Complex Numbers**.#### Is 3i a complex number?

Remember that a**complex number**has the form a + bi. You need to figure out what a and b need to be. Since −**3i**is an**imaginary number**, it is the**imaginary**part (bi) of the**complex number**a + bi. This**imaginary number**has no real parts, so the value of a is 0.

B.

### Are all irrational numbers are real numbers?

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**.#### Are all irrational numbers transcendental?

All real**transcendental numbers**are**irrational**, since all rational**numbers**are algebraic. The converse is not true: not all**irrational numbers are transcendental**; e.g., the square root of 2 is**irrational**but not a**transcendental number**, since it is a solution of the polynomial equation x^{2}− 2 = 0.#### What are the real numbers?

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**).#### Are rational numbers are real numbers?

Correct. The number is between integers, so it can't be an integer or a whole number. It's written as a ratio of two integers, so it's a**rational**number and not irrational. All**rational numbers are real numbers**, so this number is**rational**and**real**.

Updated: 18th October 2018