Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the argument of the complex number
6-2sqrt3i in the interval
0 <= theta < 2pi.
Express your answer in terms of
pi.
Answer:

Find the argument of the complex number $6-2 \sqrt{3} i$ in the interval $0 \leq \theta<2 \pi$ . $\newline$ Express your answer in terms of $\pi$ . $\newline$ Answer:

View step-by-step help

View step-by-step help

Simplify radical expressions with variables

Full solution

Q. Find the argument of the complex number

6-2 \sqrt{3} i

in the interval

0 \leq \theta<2 \pi

.

\newline

Express your answer in terms of

\pi

.

\newline

Answer:

Calculate arctan value: To find the argument of a complex number in the form $a + bi$ , where $a$ is the real part and $b$ is the imaginary part, we use the formula $\theta = \text{arctan}(\frac{b}{a})$ . The complex number given is $6 - 2\sqrt{3}i$ , so $a = 6$ and $b = -2\sqrt{3}$ .
Simplify arctan expression: First, we calculate the arctan of $b/a$ , which is $\text{arctan}(-2\sqrt{3}/6)$ . Simplifying the fraction gives us $\text{arctan}(-\sqrt{3}/3)$ .
Adjust angle for interval: The value of $\arctan(-\sqrt{3}/3)$ corresponds to the angle $-\pi/6$ , because $\tan(-\pi/6) = -\sqrt{3}/3$ . However, since we want the argument in the interval $0 \leq \theta < 2\pi$ , we need to add $2\pi$ to the negative angle to find the equivalent positive angle.
Finalize argument value: Adding $2\pi$ to $-\pi/6$ gives us the angle $11\pi/6$ , which is in the desired interval $0 \leq \theta < 2\pi$ .

More problems from Simplify radical expressions with variables

Question

\newline

\sqrt{\frac{9}{25}}

\newline

Posted 2 months ago

Question

\newline

1,000

\text{ milligrams}

\_\_\_\_

\text{ grams}

Posted 2 months ago

Question

3

-gallon bottle of bleach costs

\$11.52

. What is the price per quart?

\newline

Posted 2 months ago

Question

Maureen can't wait to make chocolate chip zucchini bread with zucchini from her garden. Her recipe calls for

8

ounces of chocolate chips per loaf. If she has enough zucchini to make

4

loaves of zucchini bread, how many pounds of chocolate chips does she need?

\newline

Hint: There are

16

1

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

Posted 2 months ago

Question

A whale is swimming due north at a speed of

30

miles per hour. Just

5

miles away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of

46

miles per hour. How long will it be before they meet? If necessary, round your answer to the nearest minute.

\_\_\_\_

\_\_\_\_

Posted 2 months ago

Question

\newline

500

=

Posted 3 months ago

Question

\newline

2,000

=

Posted 3 months ago

Question

\newline

750

=

Posted 3 months ago

Question

\newline

1,500

=

Posted 3 months ago

Question

\newline

1,500

=

Posted 3 months ago