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max2010maxim [7]
2 years ago
10

Evaluate (-1+i(root 3))^60

Mathematics
1 answer:
Elodia [21]2 years ago
8 0

Answer:

2^60.

Step-by-step explanation:

You can do this using deMoivres theorem.

First convert to Polar form:

(-1+i(root 3))^60

r = √((-1)^2 + (√3)^2)

  = √(1 + 3)

= 2.

So sin Ф = √3/2

Ф = 2π/3      -  as the angle is in the second quadrant (  real part is -1)

So in polar form we have:

[2(cos2π/3  + i sin2π/3 )]^60

Bu de Moivres theorem this is

2^60(cos2π/3* 60   + i sin2π/3* 60)

= 2^60(cos(120π/3) + i sin(120π/3)

= 2^60(cos40π + i sin 40π)

= 2^60(1 + i*0)

= 2^60.

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A) 5 x<br> = -95<br> b)<br> X<br> (-2) = 70<br> c)<br> + 10 = -18<br> d)<br> +(-3) = 27
erastovalidia [21]

Answer:

t7654

Step-by-step explanation:

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3 0
3 years ago
Part D: Your parents put in fencing around the walkway for safety. If 110 feet of
Sonbull [250]

Answer:

Step-by-step explanation:

Not near enough information to know.

I ASSUME that the pool is surrounded by a walkway of constant width (w = 2 ft, from comments)

The pool shape is important as well. No mention of  the shape

If the pool is circular and the walkway is 3 ft wide

the fence encloses a diameter of 110/π = 35 ft

so the diameter of the pool would be 35 - 2(3) = 29 ft.

POOL IS RECTANGULAR from comments

If the pool is square and the walkway is 2 ft wide, each side of the fence is

110 / 4 = 27.5 ft and the pool would be 27.5 - 2(2) = 23.5 ft on a side.

There are an infinite number of rectangular width and length dimensions and walkway dimensions which would result in a fence length of 110 ft.

Edit from comments

Still an infinite number of rectangular length an width dimensions for a pool with a 2 ft wide walkway around it.

Let's say that we are told the pool is 12 ft wide with 2 ft walkway.

Let L be the pool length

110 = 2(12 + 2(2)) + 2(L + 2(2))

110 = 32 + 2L + 8

70 = 2L

L = 35 ft

8 0
3 years ago
A band leader randomly selects 2 students out of 80 band members. If you and your brother are both band members. What is the pro
larisa [96]

The probability of choosing one of us is      2 / 80 .

If that happens, then the probability of choosing
the other one is  1 / 79 .

The probability of both things happening is

        (2/80) x (1/79) =  1/3160  =  0.0003165... = 0.032... percent
 
6 0
3 years ago
Rewrite in simplest terms: (10x-5)-(8x-6)
fredd [130]

Answer:

2x-1

Step-by-step explanation:

(10x-5)-(8x+6)

10x-8x-5+6

2x-1

4 0
2 years ago
4(x+x+7)-2x+8-4 substitute x=1 and x=2
Travka [436]
4(x+x+7)-2x+8-4
Substitute x with 1
4(1+1+7)-2(1)+8-4
=4(2+7)-2+4
=4(9)-2+4
=36-2+4
=34+4
=38

4(x+x+7)-2x+8-4
Substitute x with 2
4(2+2+7)-2(2)+8-4
=4(4+7)-4+4
=4(11)
=44. Hope it help!
3 0
3 years ago
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