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
masya89 [10]
3 years ago
8

Find the complex fourth roots \[-\sqrt{3}+\iota \] in polar form.

Mathematics
1 answer:
____ [38]3 years ago
7 0

Let z=-\sqrt3+i. Then

|z|=\sqrt{(-\sqrt3)^2+1^2}=2

z lies in the second quadrant, so

\arg z=\pi+\tan^{-1}\left(-\dfrac1{\sqrt3}\right)=\dfrac{5\pi}6

So we have

z=2e^{i5\pi/6}

and the fourth roots of z are

2^{1/4}e^{i(5\pi/6+k\pi)/4}

where k\in\{0,1,2,3\}. In particular, they are

2^{1/4}e^{i(5\pi/6)/4}=2^{1/4}e^{i5\pi/24}

2^{1/4}e^{i(5\pi/6+2\pi)/4}=2^{1/4}e^{i17\pi/24}

2^{1/4}e^{i(5\pi/6+4\pi)/4}=2^{1/4}e^{i29\pi/24}

2^{1/4}e^{i(5\pi/6+6\pi)/4}=2^{1/4}e^{i41\pi/24}

You might be interested in
[55 POINTS] Did I match these like terms correctly?
Sergeeva-Olga [200]
Yea you did jsixidjdjiejs
8 0
3 years ago
Miko’s restaurant bill was $16. She used the expression 1.18(16) to find the total cost including an 18% tip.
Lena [83]

The answer is (1+0.18)16.

3 0
3 years ago
Read 2 more answers
The picture this is math 1 for apex learning
noname [10]

Answer:

C.

Step-by-step explanation:

(f+g)(x) ➡ f(x) + g(x)

x/2 - 2 + 2x^2 + x - 3 = 2x^2 + 3x/2 -5

3 0
3 years ago
Normal six-sided dice have a different number of pips on each face, from 1 to 6. You roll two such dice and add the result.
NARA [144]

Answer:

1) 16.7% probability of rolling 10+.

2) 50% probability an odd number is rolled.

3) 7 is the most likely total result.

Step-by-step explanation:

These are all the possible outcomes:

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes

1) what is the probability of rolling 10+?

There are 6 possible outcomes in which 10+ is rolled:

(4,6), (5,5),(5,6), (6,4), (6,5),(6,6).

So there is a 6/36 = 0.167 = 16.7% probability of rolling 10+.

2) what is the probability of rolling an odd number?

There are 18 possible outcomes in which an odd number is rolled.

So there is a 18/36 = 0.5 = 50% probability an odd number is rolled.

3) what is the total that is most likely to result?

There are 6 outcomes in which 7 is rolled.

So 7 is the most likely total result.

6 0
3 years ago
Find the distance between (6, -7), (3, -5) round your answer to the nearest tenth
saw5 [17]

Answer:

d ≈ 3.6 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }

with (x₁, y₁ ) = (6, - 7 ) and (x₂, y₂ ) = (3, - 5 )

d = \sqrt{(3-6)^2+(-5-(-7))^2}

   = \sqrt{(-3)^2+(-5+7)^2}

   = \sqrt{9+2^2}

   = \sqrt{9+4}

    = \sqrt{13}

    ≈ 3.6 ( to the nearest tenth )

3 0
2 years ago
Other questions:
  • Find the volume of the figure. Round your answer to the nearest tenth if necessary
    10·1 answer
  • The area of a wetland drops by 1/4 every 8 years. What percent of its total area disappears after 40 years?
    11·1 answer
  • Solve for x 5x2-4x=6
    6·1 answer
  • Write your answer using only positive exponents. (-2x^6y^-2)^3
    9·1 answer
  • Sorry for no picture earlier, anyways pls help
    13·1 answer
  • Antwaun waters his lawn 3 times a week. If he watered his lawn 24 times in all, which equation could be used to find how many we
    9·2 answers
  • Use the substitution method to solve the system of equations. Enter your
    5·1 answer
  • What is the value of b? <br> -1 = b +(-11)
    11·2 answers
  • -4(-6 - 2n) = 30 + 8n
    6·1 answer
  • Is the product of - 7 and 4 less<br> than - 7,between 7 and 4, or<br> greater than 4?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!