Simplify the number using the imaginary unit i. \sqrt{-16}

Question:

Simplify the number using the imaginary unit {eq}i {/eq}.

{eq}\sqrt{-16} {/eq}

Imaginary number:

There are different kinds of numbers - real numbers, rational numbers, irrational numbers, integers, even imaginary numbers. An imaginary number is denoted by the letter {eq}i {/eq} and is the value of {eq}\sqrt{-1} {/eq}.

Answer and Explanation:

To simplify the number using the imaginary unit {eq}i {/eq} factor the radicand:

{eq}\sqrt{-16} {/eq}

{eq}\sqrt{(-1)(16)} {/eq}

{eq}4\sqrt{-1} {/eq}

{eq}4i {/eq}

The expression {eq}\sqrt{-16} {/eq} when simplified using {eq}i {/eq} is {eq}4i {/eq}.


Learn more about this topic:

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What is an Imaginary Number?

from Math 101: College Algebra

Chapter 5 / Lesson 1
60K

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