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
Gennadij [26K]
3 years ago
13

Hi, I am new to this website :) I'm currently taking an online trig class on De Moivre's theorem and I don't understand it at al

l! The question is: Write each expression in the standard form for a complex number, a+bi.
1. [3cos(27))+isin(27)]^5
2. [2(cos(40))+isin(40)]^6
any info regarding this question would be extremely helpful! Thanks!
Mathematics
1 answer:
Vladimir [108]3 years ago
7 0
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.

For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes

[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))] 

it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.

For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)

[2^6(cos(40*6))+isin(40*6)],

[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)

And the answer is -32 -32 √3 i

Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i

You might be interested in
Help will mark brainliest
nlexa [21]

Answer:

d

Step-by-step explanation:

8 0
3 years ago
The mass of the sun is 21.3525×102921.3525×1029 kg. the mass of mercy is 328.5×1021328.5×1021 kg.how many times larger is the ma
Liono4ka [1.6K]
This is basically a simple problem to understand. The only thing that needs to be done is to divide the mass of the sun by the mass of mercury. It will give the required result.

Number of times the mass of sun is greater than
the mass of mercury =  21.3525×102921.3525×1029/<span>328.5×1021328.5×1021
                                  = </span><span>7.1783629e+15
I hope that this is the answer that you were looking for and it has come to your great help.</span>
8 0
3 years ago
SOMEONE PLEASE ANSWER THIS ASAP RN FOR BRAINLIEST!!!!!
ololo11 [35]

Answer:

The answer would be d(c(x)) = .60x - 5

Step-by-step explanation:

In order to write an equation for d(c(x)), start with the d(y) equation.

d(y) = .80y - 5

Now input the c(x) equation in for y and then solve.

d(c(x)) = .80(.75x) - 5

d(c(x)) = .60x - 5

7 0
2 years ago
Write 805 076 using powers of 10
Artemon [7]
805076= 8.05076 x 10^5
7 0
3 years ago
////////////// 3x^2-4-x=0
Lelechka [254]

Answer:= -1

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • WILL GIVE 5 STARS / BRAINLIEST ANSWER IF GIVEN THE CORRECT ANSWER.
    5·1 answer
  • Round .593 to the nearest tenths place value.
    12·1 answer
  • Maurice bought 16.1 yards of material for costumes for a play. If each costume used 2.3 yards of material, how many costumes is
    5·1 answer
  • 2. The student council at Camp Creek Middle School determines that 3 out of 4
    10·1 answer
  • Donal currently has 7,200 points in his fantasy baseball league, which is 20% more point than Scott how many points does scott h
    14·1 answer
  • Directions: Express each equation in terms of the indicated variable then answer the questions
    9·1 answer
  • Can someone help me
    10·1 answer
  • WILL MARK BRAINLIEST PLEASE HELP
    10·1 answer
  • HELPPPPPP!!!<br><br> find each missing length. give all answers in the simplest radical form.
    5·1 answer
  • Write the expression in simpliest form WILL MARK BRAINLIEST<br> 8 ( -3x + 2)
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!