Write each number as the product of a real number and i. √-10

Key Concepts

Imaginary Numbers

Imaginary numbers are defined as multiples of the imaginary unit 'i', where i is the square root of -1. They are used to extend the real number system to solve equations that do not have real solutions, such as x^2 + 1 = 0. In this context, imaginary numbers allow us to express the square roots of negative numbers.

Complex Numbers

Complex numbers are numbers that have both a real part and an imaginary part, typically expressed in the form a + bi, where a is the real part and b is the coefficient of the imaginary part. They are essential in various fields of mathematics and engineering, providing a comprehensive way to represent and manipulate numbers that include both real and imaginary components.

Square Roots of Negative Numbers

The square root of a negative number cannot be expressed as a real number, as no real number squared gives a negative result. Instead, we use imaginary numbers to represent these square roots. For example, √-10 can be rewritten as √10 * √-1, which simplifies to √10 * i, illustrating how we can express negative square roots in terms of imaginary numbers.