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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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In mathematics, an inequality is a relation that makes a non-same comparison between two numbers or different mathematical expressions. It is used most often to examine numbers on the quantity line by using their length.

Inequality, In mathematics, is a declaration of an order relationship—greater than, extra than or same too, much less than, or much less than or identical to—between numbers or algebraic expressions.

The definition of inequality is a difference in length, amount, exceptional, social function, or another component. An instance of inequality is if you have ten of something and a person else has none.

Let t be the number.

We know that,

The phrase "5 more than a number t" is equal to adding the number t and 5

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Less represent the symbol " < ".

Therefore,

The inequality that represents this problem is 9(t+5) < 6.

Learn more about inequality here brainly.com/question/11613554

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1 year ago
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Step-by-step explanation:

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