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STatiana [176]
2 years ago
6

Can someone please help me

Mathematics
1 answer:
Dmitrij [34]2 years ago
3 0
I can’t help with this sorry out of my move set
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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
What is the fourth term in the expansion of (x + 2y)^8?
Hatshy [7]
Base on my calculation and the simplification of the form and finding its 4th power of the x+2y, i came up with a solution and finally found an answer of B. 448x^5y^3, I hope i answer your questions directly and please feel free to ask for more and ask for clarifications
4 0
3 years ago
Please help! I’ll mark brainliest
OLga [1]
The answer would be 6
8 0
2 years ago
Blank a function is the same as moving a function
earnstyle [38]

Answer:

Shifting/Translating the function

Step-by-step explanation:

8 0
3 years ago
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The perimeter of this rectangle is 24cm. If the length is 8 cm, what is the height?
Gemiola [76]

Answer:

4

Step-by-step explanation:

P = s+s+s+s

length = 8

8x2=16

24-16=8

8 / 2 = 4

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3 years ago
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