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
SpyIntel [72]
3 years ago
10

Write [2(cos15*+isin15*)]^3 in standard form a+bi

Mathematics
2 answers:
Marysya12 [62]3 years ago
8 0
Hello : 
by moivre theorem : 
[2(cos15*+isin15*)]^3 = 2^3(cos(3×45*)+isin(3×45*))
                                   =8 (cos45*+isin45*)
                                   = 8 ( √2/2 +i √2/2)
                                   = 4√2 + 4√2 i ..... ( <span>in standard form a+bi)
</span>a = b = 4√2 
Luda [366]3 years ago
6 0
<h2>Answer:</h2>

Hence, the standard form of the given expression is:

       [2(\cos 15+i\sin 15)]^3=4\sqrt{2}+4\sqrt{2}i

<h2>Step-by-step explanation:</h2>

We have to represent the expression:

[2(\cos 15+i\sin 15)]^3 in the standard form: a+bi

Now, this expression could also be written as:

[2(\cos 15+i\sin 15)]^3=2^3(\cos 15+i\sin 15)^3

i.e.

[2(\cos 15+i\sin 15)]^3=8(\cos 15+i\sin 15)^3

Now we will use the De Movier's Theorem that:

(\cos \theta+i\sin \theta)^n=\cos n\theta+i\sin n\theta

Hence, we have:

[2(\cos 15+i\sin 15)]^3=8(\cos (15\times 3)+i\sin (15\times 3))

i.e.

[2(\cos 15+i\sin 15)]^3=8[\cos 45+i\sin 45]

i.e.

[2(\cos 15+i\sin 15)]^3=8[\dfrac{1}{\sqrt{2}}+i\dfrac{1}{\sqrt{2}}]

i.e.

[2(\cos 15+i\sin 15)]^3=\dfrac{8}{\sqrt{2}}+i\dfrac{8}{\sqrt{2}}

i.e.

[2(\cos 15+i\sin 15)]^3=4\sqrt{2}+4\sqrt{2}i

You might be interested in
When graphing an inequality on a number line, an open circle means which of the following?
Sliva [168]

Answer:

Does NOT include the number the circle is placed on

Step-by-step explanation:

I don't see the answer choices that you have, so this is the best I could do! Hoped it helped!

4 0
3 years ago
Read 2 more answers
The following information is known about a loan. Time = 8 years Interest rate = 14% Principal = $1,010 What is the total amount
nadya68 [22]

❤ <em>Hey There!! ❤</em>

<em>The answer is below!!</em>

----------------------------------------------------------------------------------------------------

Step-by-step explanation:

1010 x 14 ÷ 100 x 8 = $1131.2 or $1,131.20

<em>P.S </em><em>Tell me if this is wrong...</em>

GoodLuck!!

#Be Bold

#LearnWithBrainlyAlways

_{Loserbrazts}

7 0
3 years ago
Read 2 more answers
Make a tree diagram to show sample space. Then select the total number of outcomes.
34kurt
The answer is 20 not 5 or 15 or 10
5 0
3 years ago
Read 2 more answers
What is the value of s and the length of side BC if ABCD is a rhombus?
Natali5045456 [20]

Step 1

<u>Find the value of s</u>

we know that

In a Rhombus all sides are congruent

so

AB=BC=CD=DA

AB=9s+29\\CD=10s-16

equate AB and CD

9s+29=10s-16\\

Combine like term

10s-9s=29+16\\

s=45\ units

<u>The answer Part a) is</u>

the value of s is 45\ units

Step 2

<u>Find the value of side AB</u>

AB=9s+29

substitute the value of s

AB=9*45+29=434\ units

Remember that the sides are congruent

AB=BC=CD=DA

therefore

<u>the answer Part b) is</u>

The length of the side BC is 434\ units


4 0
3 years ago
Read 2 more answers
Coach barron bought 66 pounds of ice cream for the end of the year little league social. there are 8 teams, each with 12 people.
frozen [14]
Each person gets about 9.75 ounces of ice cream 
4 0
3 years ago
Other questions:
  • The Distributive Property to express 14 + 63
    15·1 answer
  • List all the factor pairs of 48
    13·2 answers
  • A bucket holds 121.4 ounces (oz) of water when full. The bucket loses 0.04 oz of water per second. In how many seconds will the
    10·1 answer
  • Renata and david want to cover the walls in one room of their house with wall paper.
    10·1 answer
  • What are two terms that add together to make -7 and that also multiply to make 6
    13·2 answers
  • What is the equation of the line?
    11·1 answer
  • Pre-calc <br> What is the remainder when x +4 is divided by x - 2?
    5·1 answer
  • Help asap!!! 50 points total if u get big brain! elect the expressions that are equivalent to 10 + 2x + 5y + 3x.
    15·2 answers
  • Help please? giving brainliest!
    15·1 answer
  • Alberto made the box-and-whisker
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!