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
8_murik_8 [283]
3 years ago
8

Use DeMoivre's theorem to evaluate the expression

Mathematics
1 answer:
natima [27]3 years ago
7 0

Answer:

B. \dfrac{9}{2}-i\dfrac{9\sqrt{3}}{2}

Step-by-step explanation:

DeMoivre's theorem:

If the complex number z=r(\cos \alpha+i\sin\alpha), then for natural number n

z^n=r^n(\cos n\alpha+i\sin n\alpha).

In your case,

z=\sqrt{3}\left(\cos\dfrac{5\pi}{12}+i\sin\dfrac{5\pi}{12}\right)

and you have to evaluate z^4.

By DeMoivre's theorem,

z^4=(\sqrt{3})^4\left(\cos 4\cdot \dfrac{5\pi}{12}+i\sin 4\cdot \dfrac{5\pi}{12}\right)=9\left(\cos \dfrac{5\pi}{3}+i\sin\dfrac{5\pi}{3}\right)=9\left(\dfrac{1}{2}-i\dfrac{\sqrt{3}}{2}\right)=\dfrac{9}{2}-i\dfrac{9\sqrt{3}}{2}.

You might be interested in
Is the distance around a circle . You calculate the of a circle by multiplying the diameter by 3.14
anzhelika [568]
Distance around a circle is CIRCUMFERENCE
DIAMETER*PI=CIRCUMFERENCE
7 0
3 years ago
How do you solve 8x-7= 3x 9?
gtnhenbr [62]
8x - 7 = 3x + 9
8x - 3x = 9 + 7
5x = 16
x = 16/5 = 3 1/5
3 0
3 years ago
SOLVEEEE NOWWWWW HURRRYYYYYY
Sati [7]
I believe it’s a negative slope
7 0
3 years ago
Ramon has started a workout program. On Monday, he did 10 push-ups. On Tuesday, he did 13 push-
nevsk [136]

Answer:

he will do 19 pushups

Step-by-step explanation:

He will do 19 push ups because the pattern Is going up by 3 each days so if you add 3 to 16 you will get 19!!!!!

Hope This Helped :)

7 0
3 years ago
Read 2 more answers
What are the solutions of the inequality? x/5 _>-2
nata0808 [166]
X is greater than -10
5 0
3 years ago
Other questions:
  • On a map, 180 miles are represented by 4 inches. How many miles are represented by 6 inches ?
    15·2 answers
  • Pooja's plant began sprouting 222 days before Pooja bought it, and she had it for 989898 days until it died. At its tallest, the
    6·2 answers
  • Using the figure below, select the pair(s) of supplementary angles. (HINT** they may be more than 1 correct answer)
    13·2 answers
  • timmy writes the equation f(x) = x – 1. He then doubles both of the terms on the right side to create the equation g(x) = x – 2.
    9·1 answer
  • Help pls ill love you forever
    13·1 answer
  • A business has a 200 ft wall and places 6 letters on the center of an exterior wall to spell sale. if there is 1 ft betweeen eac
    13·1 answer
  • What is the solution to the system of equations?
    7·2 answers
  • 2w(w2 + 3w - 5) + 3w3 + 2(w2 + 1)
    10·1 answer
  • Simplify to a single power of 3:<br><br> 3^6 x 3
    13·1 answer
  • There are a total of 71 students in the cafeteria.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!