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Ainat [17]
3 years ago
11

What are the fourth roots of 6+6√(3i) ?

Mathematics
1 answer:
Helen [10]3 years ago
8 0

Answer:

Step-by-step explanation:

The genral form of a complex number in rectangular plane is expressed as z = x+iy

In polar coordinate, z =rcos ∅+irsin∅ where;

r is the modulus = √x²+y²

∅ is teh argument = arctan y/x

Given thr complex number z = 6+6√(3)i

r = √6²+(6√3)²

r = √36+108

r = √144

r = 12

∅ = arctan 6√3/6

∅ = arctan √3

∅ = 60°

In polar form, z = 12(cos60°+isin60°)

z = 12(cosπ/3+isinπ/3)

To get the fourth root of the equation, we will use the de moivres theorem; zⁿ = rⁿ(cosn∅+isinn∅)

z^1/4  = 12^1/4(cosπ/12+isinπ/12)

When n = 1;

z1 =  12^1/4(cosπ/3+isinn/3)

z1 = 12^1/4cis(π/3)

when n = 2;

z2 = 12^1/4(cos2π/3+isin2π/3)

z2 = 12^1/4cis(2π/3)

when n = 3;

z2 = 12^1/4(cosπ+isinπ)

z2 = 12^1/4cis(π)

when n = 4;

z2 = 12^1/4(cos4π/3+isin4π/3)

z2 = 12^1/4cis(4π/3)

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3 years ago
Tan theta= -3/4, angle theta in Quadrant IV
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3 years ago
Please help ASAP!! 31 points and brainliest!
jolli1 [7]

A relation is a function if it has only One y-value for each x-value. Functions f(2/3)=2/9 for f(x)=2x²-4x+2 and f(1/4)==-21/4 for  f(x)=4x²+2x-6

<h3>What is a function?</h3>

A relation is a function if it has only One y-value for each x-value.

The given function is

f(x)=2x²-4x+2

Put x=2/3

f(2/3)=2(2/3)²-4(2/3)+2

=2(4/9)-8/3+2

=8/9-8/3+2

=(8-24+18)/9

f(2/3)=2/9

Now f(x)=4x²+2x-6

Put x=1/4

f(1/4)=4(1/4)²+2(1/4)-6

=4/16+2/4-6

=1/4+1/2-6

= 1+2-24/4

f(1/4)==-21/4

Hence functions f(2/3)=2/9 for f(x)=2x²-4x+2 and f(1/4)==-21/4 for  f(x)=4x²+2x-6

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3 0
1 year ago
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elena55 [62]
All you do is add up the sides of the walls, and you get your answer.

<3.

OG.
8 0
2 years ago
Read 2 more answers
What is the area of a sector with a central angle of 210 degrees and a diameter of 4.6m?
WINSTONCH [101]
Sector area = (central angle / 360) * PI * radius^2
sector area = (210 / 360) * PI * 2.3^2
sector area = (7 / 12) * PI * 5.29
<span><span><span>sector area = 9.6944313302 </span> </span> </span>
<span>sector area = 9.7 square meters (rounded)

Source:
http://www.1728.org/radians.htm

</span>
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3 years ago
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