Write each number as the product of a real number and i. -√-18

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 thus √-18 can be expressed as √(18) * √(-1) = 3√2 * i.

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, -√-18 can be rewritten as a complex number, specifically 0 - 3√2 * i, where the real part is 0.

Properties of Square Roots

The properties of square roots state that √(a * b) = √a * √b, and this can be applied to negative numbers by separating the real and imaginary components. When dealing with negative values under a square root, it is essential to factor out -1 to express the result in terms of 'i'. This property is crucial for simplifying expressions involving square roots of negative numbers.