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masya89 [10]
3 years ago
8

Find the complex fourth roots \[-\sqrt{3}+\iota \] in polar form.

Mathematics
1 answer:
____ [38]3 years ago
7 0

Let z=-\sqrt3+i. Then

|z|=\sqrt{(-\sqrt3)^2+1^2}=2

z lies in the second quadrant, so

\arg z=\pi+\tan^{-1}\left(-\dfrac1{\sqrt3}\right)=\dfrac{5\pi}6

So we have

z=2e^{i5\pi/6}

and the fourth roots of z are

2^{1/4}e^{i(5\pi/6+k\pi)/4}

where k\in\{0,1,2,3\}. In particular, they are

2^{1/4}e^{i(5\pi/6)/4}=2^{1/4}e^{i5\pi/24}

2^{1/4}e^{i(5\pi/6+2\pi)/4}=2^{1/4}e^{i17\pi/24}

2^{1/4}e^{i(5\pi/6+4\pi)/4}=2^{1/4}e^{i29\pi/24}

2^{1/4}e^{i(5\pi/6+6\pi)/4}=2^{1/4}e^{i41\pi/24}

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muminat

Answer:

1. 12x^2-13.4x-11

- Degree: 2

- Number of terms: 3

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 - Degree: 3

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- Degree: 4

- Number of terms: 2

Step-by-step explanation:

For this exercise you need to remember the multiplication of signs:

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1. Given:

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Apply the Distributive property:

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Add the like terms:

=12x^2-13.4x-11

You can idenfity that:

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2. Given:

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Add the like terms:

=187 + 7x^3 - 25 + 6=7x^3+168

You can idenfity that:

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3. Given:

(3x^2 - 3)(3x^2 + 3)

Apply Distributive property:

=9x^4-9x^2+9x^2-9

Add the like terms:

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3 years ago
What sets of numbers do -7/10 belong to
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Step-by-step explanation:

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x + 7/2 = 0

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