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
Tanya [424]
3 years ago
7

For questions 13-15, Let Z1=2(cos(pi/5)+i Sin(pi/5)) And Z2=8(cos(7pi/6)+i Sin(7pi/6)). Calculate The Following Keeping Your Ans

wer In Polar Form. 13. z1z2 14. z2 15. z1/z2
Mathematics
1 answer:
weqwewe [10]3 years ago
8 0

Answer:

Step-by-step explanation:

Given the following complex values Z₁=2(cos(π/5)+i Sin(πi/5)) And Z₂=8(cos(7π/6)+i Sin(7π/6)). We are to calculate the following complex numbers;

a) Z₁Z₂ = 2(cos(π/5)+i Sin(πi/5)) * 8(cos(7π/6)+i Sin(7π/6))

Z₁Z₂ = 18 {(cos(π/5)+i Sin(π/5))*(cos(7π/6)+i Sin(7π/6)) }

Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)+i²Sin(π/5)Sin(7π/6)) }

since i² = -1

Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)-Sin(π/5)Sin(7π/6)) }

Z₁Z₂ = 18{cos(π/5)cos(7π/6) -Sin(π/5)Sin(7π/6) + i(cos(π/5)sin(7π/6)+ Sin(π/5)cos(7π/6)) }

From trigonometry identity, cos(A+B) = cosAcosB - sinAsinB and  sin(A+B) = sinAcosB + cosAsinB

The equation becomes

= 18{cos(π/5+7π/6) + isin(π/5+7π/6)) }

= 18{cos((6π+35π)/30) + isin(6π+35π)/30)) }

= 18{cos((41π)/30) + isin(41π)/30)) }

b) z2 value has already been given in polar form and it is equivalent to 8(cos(7pi/6)+i Sin(7pi/6))

c) for z1/z2 = 2(cos(pi/5)+i Sin(pi/5))/8(cos(7pi/6)+i Sin(7pi/6))

let A = pi/5 and B = 7pi/6

z1/z2 = 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B))

On rationalizing we will have;

= 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B)) * 8(cos(B)-i Sin(B))/8(cos(B)-i Sin(B))

= 16{cosAcosB-icosAsinB+isinAcosB-sinAsinB}/64{cos²B+sin²B}

= 16{cosAcosB-sinAsinB-i(cosAsinB-sinAcosB)}/64{cos²B+sin²B}

From trigonometry identity; cos²B+sin²B = 1

= 16{cos(A+ B)-i(sin(A+B)}/64

=  16{cos(pi/5+ 7pi/6)-i(sin(pi/5+7pi/6)}/64

= 16{ (cos 41π/30)-isin(41π/30)}/64

Z1/Z2 = (cos 41π/30)-isin(41π/30)/4

You might be interested in
What is csc ( Reduce fractional answers to lowest terms.
harina [27]

Answer:

cscA = \frac{5}{4}

Step-by-step explanation:

Using the identity

csc x = \frac{1}{sinx} , then

sinA = \frac{opposite}{hypotenuse} = \frac{BC}{AB} = \frac{8}{10} = \frac{4}{5} , thus

cscA = \frac{1}{\frac{4}{5} } = \frac{5}{4}

4 0
3 years ago
Find the product. Write your answer in<br> exponential form.<br> 6^-4•6^-9
Karolina [17]

Answer:

6^-13

Step-by-step explanation:

The rule for multiplying numbers with the same base but different exponents is a^b*a^c=a^(b+c), so in this case we have 6^(-4+(-9)) which is 6^-13

Hope this helped!

6 0
3 years ago
On which surface is the student unable to apply enough force to overcome the force of friction
Maurinko [17]

Rough surfaces

Ex=carpet

7 0
3 years ago
Beth wants to paint the four walls of her rectangular bedroom. Her room is 10 feet wide, 13 feet long, and 8 feet high. She will
Marat540 [252]

Answer:The answer is 1040

6 0
2 years ago
Read 2 more answers
Pls help me i’ll give u a brainlest
TEA [102]

Answer:

6 inches

Step-by-step explanation:

The volume of a box can be calculated with the simple formula l\cdot w\cdot h, where l represents length, w represents width, and h represents height. You know that 6\cdot 13\cdot h=468, so dividing both sides by 13 and 6 yields h=6 inches. Hope this helps!

7 0
2 years ago
Read 2 more answers
Other questions:
  • Which of the following is an arithmetic sequence?–20, –25, –30, –35, –45, ...
    8·2 answers
  • An advertisement for a new toothpaste claims that it reduces cavities of children in their cavity-prone years. Cavities per year
    12·1 answer
  • A rectangular garden is 8 ft wide and 15 ft long. A diagonal path cuts through the garden. How long is the path?
    14·1 answer
  • Either enter an exact answer in terms of foe use 3.14 for a
    8·1 answer
  • Kelly is using a bucket to fill up a beer with water from a well. the barrel holds 25.5 liters. the bucket holds 800 millimeters
    9·1 answer
  • Determine how many significant figures are in the number. 1. 150 2. 99.01 3. 200.1 4. 1000000
    10·1 answer
  • An Electrician charges $30 for a service call plus $75 per hour of service. If he charged 210 how many hours did he work?
    13·1 answer
  • Which of the following is the best example of a long-term goal?
    8·1 answer
  • Parallelogram is 42squared height is 7m whats the base
    9·2 answers
  • What is the value of 11 with a exponit of 4
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!