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}.

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}.