By using <span>De Moivre's theorem:
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If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴
![\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bz%7D%20%3D%20%20%5Csqrt%5Bn%5D%7Ba%7D%20%5C%20%28cos%20%5C%20%20%5Cfrac%7B%5Ctheta%20%2B%20360K%7D%7Bn%7D%20%2B%20i%20%5C%20sin%20%5C%20%5Cfrac%7B%5Ctheta%20%2B360k%7D%7Bn%7D%20%29)
k= 0, 1 , 2, ..... , (n-1)
For The given complex number <span>⇒ z = 81(cos(3π/8) + i sin(3π/8))
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Part (A) <span>
find the modulus for all of the fourth roots </span>
<span>∴ The modulus of the given complex number = l z l = 81
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∴ The modulus of the fourth root =
Part (b) find the angle for each of the four roots
The angle of the given complex number =

There is four roots and the angle between each root =

The angle of the first root =

The angle of the second root =

The angle of the third root =

The angle of the fourth root =
Part (C): find all of the fourth roots of this
The first root =

The second root =

The third root =

The fourth root =
Answer:
x² - 30 + 5x
Step-by-step explanation:
(x + 5)(x − 5)
=x(x − 5)+5(x − 5)
=x² - 5 + 5x - 25
=x² - 30 + 5x
Answer:
B, 224in2
It may get tedious but just find the area of each face and write them down
Step-by-step explanation:
Answer:
22.5 hours
Step-by-step explanation:
191.25 divided by 8.50 hours will get you the total amount of hours she worked
Answer: 3 : 2
Step-by-step explanation:
Let A represents the total population of country A and B represents the total population of country B.
According to the question,

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But, Again according to the question,
The total population that claims that they are from A = one half of the total population of A and B.
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