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
PLZ ANSWER ASASP ALMOST DUE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Burka [1]

Answer:

D) The third side could be 4 meters long.

Step-by-step explanation:

The third side of a triangle must be greater than the difference and less than the sum of the other two sides.

5-4=1

5+4=9

So the third side must be GREATER THAN 1 and LESS THAN 9.  (1<x<9)

Therefore, the answer can't be A or C.  The second one <em>could </em>be correct, depending on how much less than 4 it is.  But the last one is definitely correct.

5 0
3 years ago
Answer the following and SHOW YOUR SOLUTION.
Ivahew [28]

Answer: i need more information

Step-by-step explanation:

5 0
2 years ago
ALGEBRICAL EXPRESSIONS <br> SIMPLIFY<br><br>(7x+8y)² - (7x-8y)²<br>​
Rzqust [24]

Step-by-step explanation:

hope it helps you

mark me as brainliest

4 0
3 years ago
The end points of AB are A(-2,-3) , B(3,2) point C lies on AB and is 2/5 of the way from A to . What is the coordinates of point
JulsSmile [24]
X = x1+rx2/1+r ; y = y1+ry2/1+r   donde r es la razón 
aplicando la formula anterior las coordenadas serian x= -4/7 ; y=-11/7
donde x1 es la primera componente de punto A x2 la segunda componente del punto A y así mismo con Y<span />
6 0
3 years ago
Read 2 more answers
What is the measure of &lt;A​
Alecsey [184]

Answer:

98 degrees.

Step-by-step explanation:

The opposite angles of a cyclic quadrilateral add up to 180 degrees.

So m <A + 82 = 180

m<A = 180 - 82 = 98 degrees.

6 0
3 years ago
Other questions:
  • Solve:<br> (x+10) - (x-1)
    9·1 answer
  • What are the coordinates of the x-intercept of the equation -5y=4-2x?
    9·1 answer
  • Number 5. Please help
    8·1 answer
  • I really need help plz
    5·1 answer
  • Jenna used 32 cups of a recipe to make lunch for a party. If Jenna made half a recipe of punch, how many quarts of fruit punch d
    5·1 answer
  • The following chart shows the times of runners in the 100 meter sprint.
    11·1 answer
  • -3x minus 2 minus -6x = -4 minus -4x plus 12
    9·1 answer
  • Two vectors of lengths 4 and 6 have a dot product equal to 24. Which is true about the vectors?
    10·2 answers
  • Which equation has a value greater than -6 and less than 15?​
    8·1 answer
  • PLEASE HELP PLEASE PLEASE
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!