PLEASE ILL GIVE BRAINLIEST GIVE ME y=mx+b FORM

Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

BartSMP [9]

By using De Moivre's theorem:

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 ⇒ z = 81(cos(3π/8) + i sin(3π/8))


Part (A) find the modulus for all of the fourth roots

∴ The modulus of the given complex number = l z l = 81

∴ 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

Which of the following formulas would find the surface area of a right cylinder where h is the height, r is the radius, LA is th

Sedbober [7]

I'd say it is A but I think you have made a tpyo
It should be 2*PI*radius^2 + 2*PI*radius*height

8 0

3 years ago

If the sum of seven odd consecutive numbers is 231, find the middle number.

qaws [65]

This is your answer, good luck buddy

8 0

2 years ago

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<img src="https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%20%5Cfrac%7B7%7D%7B8%7D" id="TexFormula1" title="\sqrt{2} \frac{7}{8}" alt="\sq

quester [9]

Answer:

$\sqrt{2\frac{7}{8} } =\\\sqrt{\frac{25}{8} } =\\\sqrt{\frac{25*2}{16} } =$

±5√2/4

5 0

3 years ago

Sandy is helping her uncle at this coffee shop. She observes that, when ordering coffee, 13 of customers select chocolate flavor

otez555 [7]

Answer: The probability that 3 or more of the next 5 customers will order chocolate is 30%. 3/10

Sandy conducted her own experiment to answer this question. She observed what groups of 5 customers ordered. In her experiment, 30% of the time at least 3 of the customers ordered chocolate.

The fraction 30% is 3/10.

7 0

3 years ago

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