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dlinn [17]
3 years ago
7

What is the value of the expression when n = 3?

Mathematics
2 answers:
xz_007 [3.2K]3 years ago
8 0
Please provide the context of problem
olya-2409 [2.1K]3 years ago
3 0

Answer:

the answer is 54

Step-by-step explanation:

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Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))
BartSMP [9]
By using <span>De Moivre's theorem:
</span>
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} )
k= 0, 1 , 2, ..... , (n-1)


For The given complex number <span>⇒ z = 81(cos(3π/8) + i sin(3π/8))
</span>

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
</span>
∴ The modulus of the fourth root = \sqrt[4]{z} =  \sqrt[4]{81} = 3

Part (b) find the angle for each of the four roots

The angle of the given complex number = \frac{3 \pi}{8}
There is four roots and the angle between each root = \frac{2 \pi}{4} =  \frac{\pi}{2}
The angle of the first root = \frac{ \frac{3 \pi}{8} }{4} =  \frac{3 \pi}{32}
The angle of the second root = \frac{3\pi}{32} +  \frac{\pi}{2} =  \frac{19\pi}{32}
The angle of the third root = \frac{19\pi}{32} +  \frac{\pi}{2} =  \frac{35\pi}{32}
The angle of the  fourth root = \frac{35\pi}{32} +  \frac{\pi}{2} =  \frac{51\pi}{32}

Part (C): find all of the fourth roots of this

The first root = z_{1} = 3 ( cos \  \frac{3\pi}{32} + i \ sin \ \frac{3\pi}{32})
The second root = z_{2} = 3 ( cos \  \frac{19\pi}{32} + i \ sin \ \frac{19\pi}{32})

The third root = z_{3} = 3 ( cos \  \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})
The fourth root = z_{4} = 3 ( cos \  \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})
7 0
3 years ago
If your smart please help me answer this question .
diamong [38]

Answer:

it should be 30 or something I'm pretty sure that's the answer

8 0
2 years ago
Find one rational and one irrational no. between 3 and 5.
Leya [2.2K]
Rational number between 3 and 5 = 3.5
irrational number between 3 and 5 = (pi) ....3.14159265359.......
4 0
2 years ago
What is the surface area in square yards
MaRussiya [10]

Answer:190

Step-by-step explanation:

area of triangles is 5*3=15

15+15=30

rectangles are (5*10)*2+(6*10)=160

160+30=190

5 0
2 years ago
Which fraction correctly shows the probability of14 favorable outcomes and 37 possible outcomes?
zepelin [54]

Answer: 14/37

Step-by-step explanation:

7 0
2 years ago
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