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
blsea [12.9K]
3 years ago
7

Find the fifth roots of 32(cos 280° + i sin 280°).

Mathematics
1 answer:
Andrei [34K]3 years ago
7 0
I) Let z = 32 (cos 280 degrees + i sin 280 degrees) 
= 32 (cos (k* 360 + 280) + isin (k*360 + 280)), where k = integer
II) z^ (1/5) = (32 (cos (k*360 + 280) + i sin (k*360 + 280))) ^ (1/5)
then,
z^ (1/5) = 2(cos ((k*360 + 280)/5) + i sin((k*360 + 280)/5))
We apply De Moivre's theorem:
z^ (1/5) = 2(cos(72k + 56) + i sin (72k +56))
We can get the five roots by assigning k = 0, 1, 2, 3, and 4
When K = 0, 1st root = 2 + i sin (cos 56 + i sin 56)k = 1, 2nd root = 2 (cos 128 + i sin 128)k = 2, 3rd root = 2 (cos 200 + i sin 200)k = 3, 4th root = 2 (cos 272 + i sin 272)k = 4, 5th root = 2 (cos 344 + i sin 344)

The fifth root is 5th root = 2 (cos 344 + i sin 344)
You might be interested in
Please help i am very confused
Elena L [17]

Answer:

the mean is the average, so you would add up all the numbers and then divide by the amount of numbers

so the answer would be 67.5

8 0
3 years ago
There are 9 students in a class: 7 boys and 2girls.
AleksAgata [21]

Answer:

The probability is either 2 but mostly 3 boys.

Step-by-step explanation:

8 0
3 years ago
The length of the side opposite B measures __ units
Sindrei [870]

For this case what we should do is observe the figure.

We note that the side opposite to vertex B is the AC side.

From here, we can see that the length of the AC segment is given by:

AC = 4

Therefore, the measurement on the side opposite to vertex B is equal to 4 units.

Answer:

The length of the side opposite B measures 4 units

7 0
3 years ago
Read 2 more answers
Each chicken eats about 6 pounds of chicken feed in a month.how many pounds of chicken feed will be left after 3 months? Write a
NARA [144]
Dear Vegafred77, use 3x6=18 since a chicken eats 6 lbs of chicken.
6 0
3 years ago
PLEASE HELP 12 POINTS
stealth61 [152]
Basically subtract 59 from 709 which is 650 , halve 650 which is 325 and then add 59 to the other 325 that u have to add to the first 325 to make 650 so
709-59= 650
650\2= 325
325 + 59= 384
So 384 cheeseburgers were sold and 325 hamburgers
384+325= 709
8 0
3 years ago
Other questions:
  • May someone help me plz? Thank you!
    12·2 answers
  • Which best explains why this triangle is or is not a right triangle?
    15·2 answers
  • Tips for study better for my classes im junior
    12·1 answer
  • What is the answer to 126=14g
    9·2 answers
  • Which of the following is the graph of the quadratic function y = x2 - 4x +4?​
    5·2 answers
  • A regular octagon has side length 10.9 in. The perimeter of the octagon is 87.2 in cm and the area is 392.4 in2. A second octago
    8·2 answers
  • Y=2(x+4)+5 I need help with this question
    6·2 answers
  • Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
    6·2 answers
  • TIME REMAINING
    7·1 answer
  • You make an initial investment of $500. Fill in the table below to show how much money you would have after 3 years if your acco
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!