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1 year ago

TRIG QUESTION! De Moivre formula

Mathematics

1 answer:

gogolik [260]1 year ago

8 0

The simplification form of the complex number is Z¹⁰ = -32i because cos (17π + π/2) = 0 and sin (17π + π/2) = -1

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

It is given that:

The complex number is:

Z¹⁰ = Z⁵(cos 35π/2 + i sin 35π/2)

35π/2 = (34 + 1)π/2 = 17π + π/2

cos (17π + π/2) = -cos π/2 = 0

sin (17π + π/2) = -sin π/2 = -1

Z¹⁰ = Z⁵(0 + i [-1])

Z¹⁰ = -2⁵i

Z¹⁰ = -32i

Thus, the simplification form of the complex number is Z¹⁰ = -32i because cos (17π + π/2) = 0 and sin (17π + π/2) = -1

Learn more about the complex number here:

brainly.com/question/10251853

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Find the exact value of sin(o) a. 0.0161 b. 0.7975 c. 12/13 d. 12/5

podryga [215]

Answer:

The correct answer option is C. 12/13.

Step-by-step explanation:

We are given a right angled triangle with two known sides and we are to find the measure of the angle O.

For finding the measure of O, we will use sine for which we need to find the value of the value of the hypotenuse (MO).

$MO = \sqrt {(5)^2 + (12)^5} = \sqrt{169} = 13$

Now that we know the length of the hypotenuse, we can find sin (O).

$sin O = \frac{12}{13}$

Therefore, the correct answer option is C. 12/13.

7 0

4 years ago

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Determine whether the relation is a function. c = {(10,3), (-10, – 3), (2, - 2). (3,- 10)}

DIA [1.3K]

Yes, it is a function, because no x value is repeated.

5 0

3 years ago

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If triangle GHI is equilateral and JHK is isosceles, what is the measure of JHK

liubo4ka [24]

Answer:

The measure of JHK is 25 degrees

Step-by-step explanation:

If GHI is equilateral, it means each of the angles are equal to 60 degrees

Thus;

7x - 31 = 60

7x = 60 + 31

7x = 91

x = 91/7

x = 13 degrees

The measure of JHK IS x + 12

simply insert the value of x here

Angle JHK = 13 + 12

Angle JHK is 25 degrees

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3 years ago

The publisher of a recently released nonfiction book expects that over the first 20 months after its release, the monthly profit

wolverine [178]

Answer:

(a) $\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

(b)P'(5)=-($4.54) Thousand

(c)P'(11)=-($2.10) Thousand

(d)The fifth Month

Step-by-step explanation:

Given the monthly profit model:

$P(t)=\frac{240t-40t^2}{t^2+20}$

(a)We want to derive a model that gives the Marginal Profit, P' of the book.

We differentiate

$P(t)=\frac{240t-40t^2}{t^2+20}$ using quotient rule.

$\frac{dP}{dt}=\frac{(t^2+20)(240-80t)-(240t-40t^2)(2t)}{(t^2+20)^2}$

Simplifying

$\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

We have derived a model for the marginal profit.

(b) After 5 months, at t=5

Marginal Profit=P'(5)

$\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

$P^{'}(5)=\frac{4800-1600(5)-240(5)^2}{(5^2+20)^2}$

=-($4.54) Thousand of dollars

(c)Marginal Profit 11 Months after book release

$P^{'}(11)=\frac{4800-1600(11)-240(11)^2}{(11^2+20)^2}$

=-($2.10) Thousand of dollars

(d) Since the marginal profit at t=5 is negative, after the 5th Month, the profit starts to experience a steady decrease.

6 0

3 years ago

convert the mixed numbers to improper fractions. this will get you one step closer to finding the unit rate

Kaylis [27]

It means for example instead of writing 2 2/5 You would write 12/5
You can find out an improper fraction by simply multiplying the denominator by the front number and adding the answer to you numerator
So, 2x5= 10. 10+2= 12. So 12/5

8 0

3 years ago