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
Katen [24]
4 years ago
12

Find [5(cos 330 degrees + I sin 330 degrees)]^3

Mathematics
1 answer:
earnstyle [38]4 years ago
6 0
Given a complex number in the form:
z= \rho [\cos \theta + i \sin \theta]
The nth-power of this number, z^n, can be calculated as follows:

- the modulus of z^n is equal to the nth-power of the modulus of z, while the angle of z^n is equal to n multiplied the angle of z, so:
z^n = \rho^n [\cos n\theta + i \sin n\theta ]
In our case, n=3, so z^3 is equal to
z^3 = \rho^3 [\cos 3 \theta + i \sin 3 \theta ] = (5^3) [\cos (3 \cdot 330^{\circ}) + i \sin (3 \cdot 330^{\circ}) ] (1)
And since 
3 \cdot 330^{\circ} = 990^{\circ} = 2\pi +270^{\circ}
and both sine and cosine are periodic in 2 \pi,  (1) becomes
z^3 = 125 [\cos 270^{\circ} + i \sin 270^{\circ} ]

You might be interested in
Nine and four thousand one hundred twelve ten-thousandths
navik [9.2K]
Please specify, are we multiplying, adding, dividing or subtracting? Or am I supposed to transform these into number form?
6 0
3 years ago
Help me please someone
d1i1m1o1n [39]
The answer for this question is A
4 0
3 years ago
Read 2 more answers
I need friends this is my instragram german_escamilla57​
AlladinOne [14]

Answer:

bbbbbbbeeeeeeeeettttttttt

6 0
3 years ago
Read 2 more answers
What is the value of s in the equation 4(2s - 1) = 75 + 12?
Kruka [31]

Answer:

s=91/8

Step-by-step explanation:

  • 4(2s-1)=75+12
  • 8s-4=87
  • 8s=91
  • s=91/8
7 0
3 years ago
Read 2 more answers
ZABD and ZDBC are supplementary angles.
stellarik [79]

Answer:

Measure?

Step-by-step explanation:

Could u like explains more pls?

5 0
3 years ago
Read 2 more answers
Other questions:
  • Subtract the fractions and simplify the answer 9- 5 1/3
    5·2 answers
  • Which equation represents the line of reflection for this graph?
    10·1 answer
  • X-rays are in the ratio 2:3 for men and women. Out of 1000 x-Ray's, how many are for men ?
    9·1 answer
  • 6 for 36.00 plz help
    10·2 answers
  • What is the sum of 24 and 72? Write the answer in standard form.
    12·2 answers
  • Help! Marking Brainliest!
    11·2 answers
  • What is an equation of the line that passes through the point (-5,3) and is parallel to the line 3x-5y=30?
    13·1 answer
  • Which of the following is a unit fraction?
    12·2 answers
  • Ezra has $20 to spend on a taxi ride. The taxi company charges a flat rate of $3, plus $1.00 per mile. What is the maximum amoun
    7·1 answer
  • If you solve an equation and you end up with 0 = 6 that means the answer is 6?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!