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Stells [14]
3 years ago
8

Write the complex number in polar form:

Mathematics
1 answer:
emmasim [6.3K]3 years ago
6 0

9514 1404 393

Answer:

  2√30 ∠-120°

Step-by-step explanation:

The modulus is ...

  √((-√30)² +(-3√10)²) = √(30 +90) = √120 = 2√30

The argument is ...

  arctan(-3√10/-√30) = arctan(√3) = -120° . . . . a 3rd-quadrant angle

The polar form of the number can be written as ...

  (2√30)∠-120°

_____

<em>Additional comments</em>

Any of a number of other formats can be used, including ...

  (2√30)cis(-120°)

  (2√30; -120°)

  (2√30; -2π/3)

  2√30·e^(i4π/3)

Of course, the angle -120° (-2π/3 radians) is the same as 240° (4π/3 radians).

__

At least one app I use differentiates between (x, y) and (r; θ) by the use of a semicolon to separate the modulus and argument of polar form coordinates. I find that useful, as a pair of numbers (10.95, 4.19) by itself does not convey the fact that it represents polar coordinates. As you may have guessed, my personal preference is for the notation 10.95∠4.19. (The lack of a ° symbol indicates the angle is in radians.)

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Douglas will paint two walls in his living room. One wall is 15 feet long, and the other wall is 132 feet long. Each
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Answer:

1470 square feet

Step-by-step explanation:

15x10 =150

132×10=1320

total =1479

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What is an simplified expression for 8a-(-3-5a)-2a?
bogdanovich [222]

Answer:

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Step-by-step explanation:

Simplify the terms.

8a+3+5a-2a

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Find the interquartile range of the data.
likoan [24]

The answer is 14. Here is how I work it out.


First we are going have to identify quartile 1 and quartile 3.


So after putting the numbers in order from least to greatest mark the number with a half way point.

This is optional but it will help us spot the sections better.


31,33,35,41,43,|46,48,49,49,50

Next put parentheses around the remaining groups of numbers.

(31,33,35,41,43,)|(46,48,49,49,50)


For the next step we have to find the median of each group.


(31,33,35,41,43,)|(46,48,49,49,50)


The median of each group, are called the quartiles, the median of the lower half is quartile 1, and the median of the upper half is quartile 3.


Now subtract quartile 1 from quartile 3.


49 – 35 = 14


So the interquartile range of this data set is 14.

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