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3 years ago

Dave says:

1 answer:

8 0

There are 2 symmetry lines of a rectangle which are from its length and breadth. These two lines cut the rectangle in two similar halves which are mirror images of each other. If a rectangle is folded along its line of symmetry, it superimposes perfectly.

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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

help?‎‎‎‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎

vivado [14]

Answer:

Step-by-step explanation:

(-6,-5) , ( 0,-1) , (-3 , -3) , (2 , 0 ) are solution of the inequalities.

The point that lies on the purple area and on the solid line are the solutions of the equations.

5 0

2 years ago

Data were collected on the number of days per week that members visit a certain fitness center. The values varied from 0 to 7, a

pshichka [43]

Answer:

Step-by-step explanation:

choice A is not guaranteed since the values varied from 0 to 7.

choice B seems alright, but doesn't include about or anything about the long run.

choice C is incorrect because 50% are less than 3.12 and 50% are greater than 3.12.

choice D seems pretty good, since it says average, long run, approach, etc.

choice E is incorrect because it says "will be". It is not definite.

8 0

3 years ago

What is the reference angle for 120°?

Drupady [299]

Since the angle 240° 240 ° is in the third quadrant, the reference angle formula is Ar=Ac−180° A r = A c - 180 ° .

4 0

3 years ago

Read 2 more answers

What is the median of the data set? 15, 19, 20, 22, 26, 30, 31

Paladinen [302]

Answer:

C. 22

Step-by-step explanation:

The median is the middle number of the set if the numbers are in order from least to greatest.

This set of numbers is in order, so the median is the middle number = 22

7 0

2 years ago