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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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6 0
3 years ago
Anyone got an answer for this math question?
Dennis_Churaev [7]

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6 0
3 years ago
The width of a rectangle is 4 inches less than the length. The perimeter is 60 inches. Find the length and the
coldgirl [10]

Answer:

Length=17

width=13

Step-by-step explanation:

W=width

L=length

Perimeter = 2w+2l since it's a rectangle

W=l-4 (given)

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Perimeter =(2l-8)+2l

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6 0
3 years ago
Find MQ in parallelogram LMNQ .
Liula [17]

Answer:

MQ = 16.4

By the <u>Parallelogram Diagonals Theorem</u> , MP = <u>PQ</u>

So MQ = 2 · <u>MP</u>

<u />

Step-by-step explanation:

<u>Parallelogram Diagonals Theorem</u>

The diagonals of a parallelogram bisect each other, i.e. they divide each other into <em>two equal parts</em>.

P is the point of intersection of the diagonals.

Therefore, MP = PQ and LP = PN

If MP = 8.2, then PQ = 8.2

⇒ MQ = 8.2 + 8.2 = 16.4

8 0
2 years ago
The energy released by metabolism of 1 average candy bar is 1 x 10^6 joules.
Elis [28]

Answer: 32

Step-by-step explanation:

Given: The energy needed for 1 hour of running for an adult =4.5\times10^6\ joules.

Therefore. the energy needed for seven hours of running==7\times4.5\times10^6\ joules.=31.5\times10^6\ joules

Since, he energy released by metabolism of 1 average candy bar =1\times10^6\ joules.

Therefore, the number of candy bars an adult need to eat  to supply the energy needed for seven hours of running.=\frac{31.5\times10^6}{1\times10^6}=31.5\approx32

Hence, the adult need to eat 32 candies to supply the energy needed for seven hours of running.

3 0
2 years ago
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