How are imaginary numbers used in math?

An imaginary number is a number that, when squared, has a negative result. Essentially, an imaginary number is the square root of a negative number and does not have a tangible value. Imaginary numbers, also called complex numbers, are used in real-life applications, such as electricity, as well as quadratic equations.

How do you explain imaginary numbers to students?

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.

What grade do you learn imaginary numbers?

Students (normally in grades 10 or 11, corresponding approximately to ages 15-17) learn to add, multiply, and divide complex numbers; to solve quadratic equations with no real roots; and to find all n roots of an nth degree polynomial (usually, carefully chosen so that the rational roots theorem gets you most of the …

What are imaginary numbers give two examples?

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.

What is an example of an imaginary number?

Pure imaginary numbers The number i is by no means alone! For example, 3 i 3i 3i , i 5 i\sqrt{5} i5 ​i, square root of, 5, end square root, and −12i are all examples of pure imaginary numbers, or numbers of the form b i bi bi , where b is a nonzero real number.

How do you explain imaginary numbers to a child?

Imaginary numbers are numbers that are made from combining a real number with the imaginary unit, called i, where i is defined as . They are defined separately from the negative real numbers in that they are a square root of a negative real number (instead of a positive real number).