3 years ago

What is the constant of 12/a

Mathematics

1 answer:

Tamiku [17]3 years ago

3 0

Answer:

Step-by-step explanation:

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Express the complex number in trigonometric form. <br><br> -6 + 6 <img src="https://tex.z-dn.net/?f=%5Csqrt%7B3%7D" id="TexFor

enot [183]

Answer:

$\large\boxed{-6+6\sqrt3i=12\left(\cos\dfrac{2\pi}{3}+i\sin\dfrac{2\pi}{3}\right)}$

Step-by-step explanation:

Look at the picture.

The trigonometric form of a complex number:

$z=|z|(\cos\alpha+i\sin\alpha)$

where:

$|z|=\sqrt{a^2+b^2}\\\\\cos\alpha=\dfrac{a}{|z|}\\\\\sin\alpha=\dfrac{b}{|z|}$

We have the complex number:

$z=-6+6\sqrt3i\to a=-6,\ b=6\sqrt6$

Substitute:

$|z|=\sqrt{(-6)^2+(6\sqrt3)^2}=\sqrt{36+108}=\sqrt{144}=12$

$\cos\alpha=\dfrac{-6}{12}=-\dfrac{1}{2}\\\\\sin\alpha=\dfrac{6\sqrt3}{12}=\dfrac{\sqrt3}{2}$

Therefore

$\alpha=\dfrac{2\pi}{3}$

Finally:

$-6+6\sqrt3i=12\left(\cos\dfrac{2\pi}{3}+i\sin\dfrac{2\pi}{3}\right)$

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3 years ago

Gordon types 2,146 words in 29 minutes. Find the unit rate.

4vir4ik [10]

Commenting to ask one more question myself sorry!!

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3 years ago

Marsha earn $25 per hour up to 36 hours; after this,she is paid double time. In one particular week she earned $1550.00 .how man

mel-nik [20]

Answer: Marta worked 13 hours overtime.

Step-by-step explanation:

1): You do 25 x 36 to get the amount of money she can make before she starts to make double.

36 x 25 = 900

2): Minus $900 from $1550

$1550 - $900 = $650

3): Divide $650 by $50

$650 / $50 = 13 hours worked overtime

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3 years ago

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Ksenya-84 [330]

Answer:

The answer is the 3rd one

Step-by-step explanation:

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2 years ago

What is the approximate circumference of a circle with a diameter of 56 cm? (Use π = 3.14.) A. 351.68 cm B. 175.84 cm C. 87.92 c

laiz [17]

The answer to your question is 175.84 bc C=2(pi)r and if you plug in the numbers it equals 175.84... B hope that helped :)

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4 years ago