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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

weqwewe [10]

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

8 0

2 years ago

The maximum speed of the Tupolev Tu-144 airliner is 694m/s what is the speed in kilometers per hour

saw5 [17]

Best Answer: 694 m = 0.694 km
1hr = 3600 s
3600 × 0.694 = 2498.4 km/h

6 0

3 years ago

(5 ^ 11)/(5 ^ ?) = 5 ^ 4

katrin2010 [14]

Answer:

200

Step-by-step explanation:

55 / 5x = 20

5x=1100

x=200

6 0

2 years ago

How to do do trinomials in a easy way

Savatey [412]

Multiply the First terms
Multiply the Outside terms
Multiply the Inside term
Multiply the Last terms
Simplify

Understand factoring.

Write a space for the answer in FOIL form.
Don't write + or - between the blank terms yet, since we don't know which it will be.

Fill out the First terms.

Use factoring to guess at the Last terms.

Test which possibilities work with Outside and Inside multiplication.

Use simple factoring to make more complicated problems easier.

Look for trickier factors.

Solve problems with a number in front of the x^2.

Use substitution for higher-degree trinomials.

Check for prime numbers.

Check to see if the trinomial is a perfect square.

Check whether no solution exists.

If both binomials have the same variables to the same powers, then it is true. In general, multiplying binomials gives four terms, one corresponding to each letter of the FOIL acronym. So, you only get a trinomial when the O and I terms combine.

7 0

2 years ago

The commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH, have a waiting time during peak r

eduard

Answer:

a) height of this uniform distribution = 1/8 = 0.125.

b) P( 4 < x < 5) = (5 - 4)*0.125 = 0.125

c) P( 3 < x < 8) = (8 - 3)*0.125 = 0.625

d) P(x = 0) = 0*0.125 = 0

Step-by-step explanation:

Height of this uniform distribution is same as finding the probability for each waiting minutes.

Height of uniform distribution = 1/n. Where n is the number of occurence, in this n = 8.

a) height of this uniform distribution = 1/8 = 0.125.

Let random variable x = waiting time.

b) probability of waiting between four and five minutes

P( 4 < x < 5) = (5 - 4)*0.125 = 0.125

c) probability of waiting between three and eight minutes

P( 3 < x < 8) = (8 - 3)*0.125 = 0.625

d) probability of waiting five minutes exactly.

Since this would be just one line, and the width of the line is 0, then the

P(x = 0) = 0*0.125 = 0

8 0

2 years ago