Question

Write in terms of $i$. $$ -\sqrt{-121} $$

   Write in terms of $i$.
$$
-\sqrt{-121}
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Elayn Martin-Gay 4th Edition

Chapter 10, Problem 4

Instant Answer

Solved by Expert Dharmendra Jain

10/30/2020

Step 1

Step 1: First, we need to understand that the square root of a negative number can be expressed in terms of $i$, where $i$ is the imaginary unit with the property that $i^2 = -1$. Show more…

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Write in terms of $i$. $$ -\sqrt{-121} $$

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Key Concepts

Complex Numbers

Complex numbers extend the real number system by including numbers that have a real part and an imaginary part, usually expressed in the form a + bi. They are essential in representing the square roots of negative numbers, which do not exist within the set of real numbers.

Imaginary Unit

The imaginary unit, denoted as i, is defined by the property that i² = -1. It is a fundamental component in the field of complex numbers and is used to express the square roots of negative numbers, making it possible to simplify expressions like ?(-121).

Properties of Radicals

Radicals have properties that allow for the decomposition of the radicand into factors, particularly when one of the factors is a perfect square. In the case of square roots of negative numbers, the negative factor can be separated and expressed using the imaginary unit, facilitating the simplification of expressions to a form involving i.

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