Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $-\sqrt{-27}$

View step-by-step help

View step-by-step help

Introduction to complex numbers

Full solution

Q. Use the imaginary number

i

to rewrite the expression below as a complex number. Simplify all radicals.

-\sqrt{-27}

Express as Product: Express $-\sqrt{-27}$ as the product of square roots and $\sqrt{-1}$ . $-\sqrt{-27} = -\sqrt{-1 \times 27}$
Recognize Imaginary Unit: Recognize that $\sqrt{-1}$ is the imaginary unit $i$ . $-\sqrt{-27} = -i \times \sqrt{27}$
Simplify Prime Factors: Simplify $\sqrt{27}$ by finding the prime factors of $27$ . $\newline$ $27 = 3 \times 3 \times 3$
Express as Multiplication: Express $\sqrt{27}$ as $\sqrt{3 \times 3 \times 3}$ .
$-i \times \sqrt{27} = -i \times \sqrt{3 \times 3 \times 3}$
Take Out Square Root: Take out the square root of $9$ (which is $3$ ) from under the radical. $\newline$ $-i \sqrt{3 \times 3 \times 3} = -i \times 3 \sqrt{3}$
Multiply by $-3i$ : Multiply $-i$ by $3$ . $-i \times 3 \times \sqrt{3} = -3i \times \sqrt{3}$

More problems from Introduction to complex numbers

Question

\newline

8i + 6i

\newline

\newline

Write your answer in the form

a + bi

\newline

\underline{\hspace{1cm}}

\newline

Posted 2 months ago

Question

Find the complex conjugate of the given number.

\newline

4 + 10i

\newline

\newline

Write your answer in the form

a + bi

\newline

Posted 1 month ago

Question

\newline

\frac{{-4i}}{{-9i}}

\newline

\newline

Write your answer in the form

a + bi

. Reduce all fractions.

\newline

\_\_\_\_\_

\newline

Posted 1 month ago

Question

Combine the like terms to create an equivalent expression.

\newline

7k-k+19=\boxed{\phantom{0}}

Posted 4 months ago

Question

Apply the distributive property to factor out the greatest common factor.

\newline

9+12 n=

Posted 1 month ago

Question

Solve the equation.

\newline

\begin{aligned} & 12=n-9 \\ n= & \square \end{aligned}

Posted 4 months ago

Question

What is the amplitude of

y=-\sin (8 x-3)+5

\newline

Posted 2 months ago

Question

What is the period of

\newline

y=4 \sin (-2 x+7)-1 \text { ? }

\newline

Give an exact value.

\newline

Posted 1 month ago

Question

3 \cdot(3+20 i)=

\newline

Your answer should be a complex number in the form

a+b i

a

b

are real numbers.

Posted 3 months ago

Question

(35-23 i)+(13+25 i)=

\newline

Express your answer in the form

(a+b i)

Posted 1 month ago