Question

Write each number as a multiple of $i$. $$ \sqrt{-9} $$

   Write each number as a multiple of $i$.
$$
\sqrt{-9}
$$

Beginning Algebra

Beginning Algebra

Margaret L. Lial,… 11th Edition

Chapter 9, Problem 1

Instant Answer

Solved by Expert Julie Silva

07/02/2020

Step 1

We know that the square root of a negative number is not defined in the real number system. However, in the complex number system, we can express the square root of a negative number as a multiple of $i$ (the imaginary unit). Show more…

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Write each number as a multiple of $i$. $$ \sqrt{-9} $$

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Key Concepts

Imaginary Unit

The imaginary unit, denoted as i, is a fundamental concept in complex numbers. It is defined by the property that i² equals -1, which allows us to handle the square roots of negative numbers and extend the realm of real numbers to complex numbers.

Complex Numbers

Complex numbers are expressions of the form a + bi, where a and b are real numbers, and i is the imaginary unit. This concept expands the notion of numbers beyond the real number line and provides a framework for dealing with equations that involve the square roots of negative values.

Square Roots of Negative Numbers

Square roots of negative numbers are not defined within the set of real numbers but can be expressed in terms of the imaginary unit i. By writing the square root of a negative number as a multiple of i, such as expressing ?(-n) as ?n times i, we translate these expressions into the language of complex numbers.

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