1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
bulgar [2K]
3 years ago
15

Express the complex number in trigonometric form. -6 + 6 square root of 3 i ?

Mathematics
1 answer:
bagirrra123 [75]3 years ago
5 0
\bf \begin{array}{clclll}
-6&+&6\sqrt{3}\ i\\
\uparrow &&\uparrow \\
a&&b
\end{array}\qquad 
\begin{cases}
r=\sqrt{a^2+b^2}\\
\theta =tan^{-1}\left( \frac{b}{a} \right)
\end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\
-------------------------------\\\\

\bf r=\sqrt{(-6)^2+(6\sqrt{3})^2}\implies r=\sqrt{36+(6^2\cdot 3)}\implies r=\sqrt{144}
\\\\\\
r=12\leftarrow 
\\\\\\
\theta =tan^{-1}\left( \frac{6\sqrt{3}}{-6} \right)\implies \theta =tan^{-1}\left( -\sqrt{3}\right)\implies \theta =
\begin{cases}
\frac{2\pi }{3}\leftarrow \\
\frac{5\pi }{3}
\end{cases}

now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.

thus         \bf 12\left[cos\left( \frac{2\pi }{3} \right) +i\ sin\left( \frac{2\pi }{3} \right) \right]
You might be interested in
The amount of snowfall over 6 months in Michigan was 2, 12, 8, 18, 8, and 0 inches. find the range and median of the monthly sno
Ksenya-84 [330]

Answer:

the range is 18 and the median is 8

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
A drop in temperature of 9 degrees overnight
Rina8888 [55]
Whats the question?
8 0
2 years ago
Which of the following equations represents a line that passes through the points​
Xelga [282]

Answer:

C) I only

Step-by-step explanation:

( -1, -2) and (0,4)

Slope:

m=(y2-y1)/(x2-x1)

m=(4+2)/(0+1)

m=6/1

m=6

Slope-intercept:

y - y1 = m(x - x1)

y + 2 = 6(x + 1)

y + 2 = 6x + 6

y = 6x + 4

y - 16 = 6(x - 2)

y - 16 = 6x - 12

y = 6x + 4

6 0
3 years ago
Ariana plans to use $260 less than three-fourths of savings to buy a car. If the purchase price of the car is 9,340, how much do
tangare [24]

She has $12,488 in savings

Step-by-step explanation:

Ariana plans to use $260 less than three-fourths of savings to buy a car.

If the purchase price of the car is 9,340, we need to find how much

she has in savings

To find the savings

  • Assume that she has $x in savings
  • Write an equation of x
  • Solve the equation to find x

∵ She has $x in savings

∵ She plans to use $260 less than three-fourths of savings

- Three-fourths means \frac{3}{4} and less than means subtract

∴ She plans to use \frac{3}{4} x - 26

∵ The purchase price of the car is 9,340

- Equate the expression of x by 9,340

∴ \frac{3}{4} x - 26 = 9,340

Now let us solve the equation

∵ \frac{3}{4} x - 26 = 9,340

- Add 26 to both sides

∴ \frac{3}{4} x = 9,366

- Divide both sides by \frac{3}{4}

∴ x = $12,488

She has $12,488 in savings

Learn more:

You can learn more about word problems in brainly.com/question/3950386

#LearnwithBrainly

7 0
3 years ago
Which expression can be used to determine 50% of 42?
snow_lady [41]

Answer: 42 divided by 2

Step-by-step explanation: 50% is one half, and 42/2 is one half of 42.

4 0
3 years ago
Read 2 more answers
Other questions:
  • Write an expression to represent:<br> One minus the product of four and a number x
    11·2 answers
  • Solve 11b^2-9=-68 using the square root method
    15·1 answer
  • A publisher sells 10^6 copies of a new book. Each book has 10^2 pages. How many pages total are there in all of the books sold?
    8·1 answer
  • Help?.. I’m confused
    5·1 answer
  • Can somebody help me
    8·1 answer
  • HELP ME PLEASE I need it
    6·1 answer
  • In what ways are adding and subtracting important to use in life? PLEASE ANSWER ASAP
    12·2 answers
  • Solve 5 1/2 = b − 12 1/4.
    14·1 answer
  • The diameter of a circle is 10 cm. Find its area in terms of \piπ.
    10·1 answer
  • a family originally bought a home for $273,830. Now the home’s value is 30% higher than that. What is the value of the home now?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!