Write each number as the product of a real number and i. √-25

Key Concepts

Imaginary Numbers

Imaginary numbers are defined as multiples of the imaginary unit 'i', where i is the square root of -1. They arise when taking the square root of negative numbers, which do not have real solutions. For example, √-1 = i, and √-25 can be expressed as 5i, since √-25 = √(25) * √(-1).

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. In the context of the question, √-25 can be represented as 0 + 5i, indicating that there is no real component and the entire value is imaginary.

Properties of Square Roots

The properties of square roots state that the square root of a product can be expressed as the product of the square roots of the individual factors. This property is crucial when dealing with negative numbers, as it allows us to separate the real and imaginary components. For instance, √-25 can be rewritten as √(25) * √(-1), leading to the conclusion that √-25 = 5i.