Find each square root. See Example 1. √-121

Key Concepts

Square Roots

A square root of a number 'x' is a value 'y' such that y² = x. For positive numbers, square roots yield real numbers, while negative numbers do not have real square roots. Instead, they lead to complex numbers, which include the imaginary unit 'i', defined as √-1.

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where 'a' is the real part and 'b' is the coefficient of the imaginary unit 'i'. They arise when taking square roots of negative numbers, allowing for solutions in equations that would otherwise have none in the real number system.

Imaginary Unit (i)

The imaginary unit 'i' is defined as the square root of -1. It is a fundamental concept in complex numbers, enabling the extension of the real number system to include solutions to equations involving negative square roots. For example, √-121 can be expressed as 11i, where 11 is the square root of 121.