Question

Express in terms of $i$. $$ -\sqrt{-11} $$

   Express in terms of $i$.
$$
-\sqrt{-11}
$$

Intermediate Algebra : Concepts and Applications

Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger,… 10th Edition

Chapter 7, Problem 15

Instant Answer

Solved by Expert Sheryl Ezze

02/03/2021

Step 1

We can rewrite this as $-\sqrt{-1 \times 11}$. Show more…

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Express in terms of $i$. $$ -\sqrt{-11} $$

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Key Concepts

Imaginary Unit

The imaginary unit, denoted as i, is defined by the property i^2 = -1. This concept allows us to extend the real number system to include solutions to equations that have no real solutions, such as the square roots of negative numbers.

Square Roots of Negative Numbers

When taking the square root of a negative number, the process involves factoring out the negative sign and introducing the imaginary unit i. For instance, the square root of a negative number -a (with a > 0) can be written as i?a, thus converting an otherwise undefined real expression into a complex expression.

Complex Numbers

Complex numbers are expressions that comprise both a real component and an imaginary component. They are generally written in the form a + bi. Expressing the square root of a negative number in terms of i is a fundamental application in the field of complex numbers, enabling a complete number system that includes solutions to all polynomial equations.

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