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
aliina [53]
3 years ago
11

Find the fifth roots of 243(cos 240° + i sin 240°).

Mathematics
1 answer:
Mazyrski [523]3 years ago
7 0

Answer:

See below.

Step-by-step explanation:

Fifth root of 243 = 3,

Suppose r( cos Ф + i sinФ) is the fifth root of 243(cos 240 + i sin 240),

then r^5( cos  Ф  + i sin  Ф )^5 = 243(cos 240 + i sin 240).

Equating equal parts and using de Moivre's theorem:

r^5 =243  and  cos  5Ф  + i sin  5Ф = cos 240 + i sin 240

r = 3 and  5Ф = 240 +360p so Ф =  48 + 72p

So Ф = 48, 120, 192, 264, 336  for   48 ≤ Ф < 360

So there are 5 distinct solutions given by:

3(cos 48 + i sin 48),

3(cos 120 + i sin 120),

3(cos 192 + i sin 192),

3(cos 264 + i sin 264),

3(cos 336 + i sin 336).. (Answer).

You might be interested in
A football field is 160 ft wide. Convert the width to yards
forsale [732]
The answer is "53.33 yards"
4 0
3 years ago
Franklin walked 1/2 mile in 8 1/2 minutes. What is the unit rate in miles per minute ?
Alexus [3.1K]

.0588 miles per minute

Step-by-step explanation:

0.5/8.5 = ~.0588

8 0
3 years ago
7)
algol13

Answer: $ 38.69 ; There are 12 people in the crew

8 0
3 years ago
Can someone please help me with my homework please.p
umka2103 [35]

Answer:

8-20c

Step-by-step explanation:

Just plug 4c into the function

8-5x

8-5(4c)

8-20c

4 0
3 years ago
What the area of the triangle!<br><br><br> need help with these question would mean a lot
zloy xaker [14]
Heyy I don’t think your pictures are loading it just shows grey
3 0
3 years ago
Other questions:
  • Evaluate and simplify if possible:
    6·1 answer
  • The sum of three consecutive numbers is 72. What is the smallest of these numbers?
    14·2 answers
  • The length of the entire border of the Unites States is approximately 32,000 miles, 5 8 of which is coastline. How long is the c
    15·1 answer
  • How do you solve this? need help asap!! find y!!
    7·1 answer
  • What is the definition of prime
    11·2 answers
  • A. 3/44<br><br> B. 4/9<br><br> C. 3/11<br><br> D. 1/4
    7·1 answer
  • if the slope of a line through the origin and (-2, b) is 2, and the line through (b, -2) and (a, 5) is parallel to that line, wh
    12·1 answer
  • Can anyone help me please?
    5·2 answers
  • Can someone help with this
    5·1 answer
  • The Ramos family drove to their family reunion. Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours. Af
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!