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. $-\sqrt{-60}$

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{-60}

Express as product: First, let's express $-\sqrt{-60}$ as the product of square roots and $\sqrt{-1}$ . $\newline$ $-\sqrt{-60} = -\sqrt{-1 \times 60}$
Rewrite and simplify: Now, let's rewrite $-\sqrt{-1}$ as $i$ and $\sqrt{60}$ as $\sqrt{4\times15}$ to simplify the radical. $\newline$ $-\sqrt{-60} = -i \times \sqrt{4\times15}$
Simplify radical: We know that $\sqrt{4}$ is $2$ , so we can simplify further. $\newline$ $-i \cdot \sqrt{4\cdot15} = -i \cdot \sqrt{4} \cdot \sqrt{15}$
Do multiplication: Now, let's do the multiplication. $\newline$ $-i \times \sqrt{4} \times \sqrt{15} = -i \times 2 \times \sqrt{15}$
Final complex number: Finally, we multiply $-i$ by $2$ to get the simplified complex number. $-i \times 2 \times \sqrt{15} = -2i \times \sqrt{15}$

More problems from Introduction to complex numbers

Question

\newline

8i + 6i

\newline

\newline

Write your answer in the form

a + bi

Posted 8 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 8 months ago

Question

\newline

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

\newline

\newline

Write your simplified answer in the form

a + bi

Posted 8 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 8 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 11 months ago

Question

What is the period of

\newline

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

\newline

Give an exact value.

\newline

Posted 11 months 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 11 months ago

Related topics

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