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. $-\sqrt{-88}$

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{-88}

Breakdown of expression: First, let's break $-\sqrt{-88}$ into $-\sqrt{-1 \times 88}$ .
Use of imaginary unit: Now, we know that $\sqrt{-1}$ is the imaginary unit $i$ , so we can write $-\sqrt{-1 \times 88}$ as $-i \times \sqrt{88}$ .
Simplify $\sqrt{88}$ : Next, we simplify $\sqrt{88}$ by finding the prime factors of $88$ , which are $2$ , $2$ , $2$ , and $11$ . So, $\sqrt{88}$ is $\sqrt{2^3 \times 11}$ .
Factorize $\sqrt{88}$ : We can take out a pair of $2$ s from under the radical as a single $2$ , so $\sqrt{2^3 \times 11}$ becomes $2 \times \sqrt{2 \times 11}$ .
Final simplification: Now we have $-i \times 2 \times \sqrt{2 \times 11}$ , which simplifies to $-2i \times \sqrt{22}$ .

More problems from Introduction to complex numbers

Question

\newline

8i + 6i

\newline

\newline

Write your answer in the form

a + bi

Posted 9 months ago

Question

Find the complex conjugate of the given number.

\newline

4 + 10i

\newline

\newline

Write your answer in the form

a + bi

Posted 9 months ago

Question

\newline

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

\newline

\newline

Write your simplified answer in the form

a + bi

Posted 9 months ago

Question

Combine the like terms to create an equivalent expression.

\newline

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

Posted 1 year ago

Question

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

\newline

9+12 n=

Posted 9 months ago

Question

Solve the equation.

\newline

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

Posted 1 year ago

Question

What is the amplitude of

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

\newline

Posted 1 year ago

Question

What is the period of

\newline

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

\newline

Give an exact value.

\newline

Posted 1 year 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 1 year ago

Question

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

\newline

Express your answer in the form

(a+b i)

Posted 1 year ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant