Question

Express in terms of $i$ $$ \sqrt{-4}+\sqrt{-12} $$

   Express in terms of $i$
$$
\sqrt{-4}+\sqrt{-12}
$$

Elementary and Intermediate Algebra

Elementary and Intermediate Algebra

Marvin L. Bittinger,… 4th Edition

Chapter 10, Problem 24

Instant Answer

Solved by Expert Julie Silva

05/17/2020

Step 1

We start with $\sqrt{-4}$. The negative sign under the square root can be represented as $i$, and $4$ is a perfect square, so we can simplify this as $i \cdot 2$. Show more…

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Express in terms of $i$ $$ \sqrt{-4}+\sqrt{-12} $$

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Key Concepts

Imaginary Unit

The imaginary unit, denoted as i, is defined as the square root of -1. It allows for the extension of the real number system to the complex number system by providing a way to express the square roots of negative numbers.

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part. They are typically expressed in the form a + bi, where a and b are real numbers. This concept is important for working with expressions involving negative square roots.

Simplification of Square Roots of Negative Numbers

This concept involves rewriting the square roots of negative numbers by factoring out the negative unit. For example, ?(-a) can be expressed as ?a multiplied by the imaginary unit i. This method is essential for rewriting radicals in terms of i.

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