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Bond [772]
3 years ago
5

The answer to all of these problems

Mathematics
1 answer:
timurjin [86]3 years ago
4 0
Its easier to ask somebody face-to-face dude
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Z^5=-243i, find the solution to the equation whose argument is strictly between 180 degrees and 270 degrees. Round your answer t
11Alexandr11 [23.1K]

Answer:

The solution is z = -2.853 - i 0.927.

Step-by-step explanation:

Complex power is determined by means of the De Moivre's Theorem, whose expression is:

z^{n} = r^{n} \cdot (\cos n\theta + i \sin n\theta)

Where r is the norm of the complex number. In this case, expression can be written as:

-i 243 = 3^{5} \cdot (\cos 5\theta + i \sin 5\theta)

The real component must be equal to zero and complex component must be equal to -1. That is to say:

\cos 5\theta = 0

\sin 5\theta = -1

Possible solutions for each component are, respectively:

Real component

5\theta = \cos^{-1}0

5\theta = \frac{\pi}{2} \pm \pi\cdot j, \forall j \in \mathbb{N}_{O}

\theta = \frac{\pi}{10} \pm \frac{\pi}{5}  \cdot j, \forall j \in \mathbb{N}_{O}

Possible solutions: \frac{11\pi}{10}, \frac{13\pi}{10}, \frac{3\pi}{2}

Complex component

5\theta = \sin^{-1}(-1)

5\theta = \frac{3\pi}{2} \pm 2\pi \cdot j, \forall j \in \mathbb{N}_{O}

\theta = \frac{3\pi}{10} \pm \frac{2\pi}{5}  \cdot j, \forall j \in \mathbb{N}_{O}

Possible solutions: \frac{11\pi}{10}, \frac{3\pi}{2}

There is one solution whose argument is strictly between 180 degrees (\pi) and 270 degrees (1.5\pi).

z = 3 \cdot \left( \cos \frac{11\pi}{10} + i \sin \frac{11\pi}{10} \right)

z = -2.853 - i 0.927

6 0
3 years ago
Does the following graph represent a function?
Vilka [71]

Answer:

Yes

Step-by-step explanation:

It passes the vertical line test or pencil test which means that it only touches one point at a time.

5 0
3 years ago
At a school with 100 students, 40 students are taking Arabic, 35 Bulgarian, and 25
Ad libitum [116K]
A no students are taking all 3 languages
B 41 students are taking no language sorry if I’m wrong have a great day
4 0
3 years ago
Need help don’t understand
Arturiano [62]

Answer:

a) <EGA and <AGB

b) <FGE and <CGB

c) <FGE and <EGC

d) <FGE and <FGA

e) <CGD=55

Step-by-step explanation:

a) Supplementary angles add up to 180 degrees.

<EGA and <AGB are supplementary.

b) Vertical angles are also called X-angles. Think of them as angles in the vertically opposite corners of the letter X.

<FGE and <CGB are a pair of vertical angles

c) Adjacent angles are next to each other.

<FGE and <EGC are a pair of adjacent angles

d) Complementary angles add up to 90 degrees.

<FGE and <FGA are a pair of complementary angles

e) <CGD=<FGA because they are vertical angles.

But <EGA=90-35=55

Therefore <CGD=55

6 0
3 years ago
In circle P with MLNRQ =60, find the mLNPQ
Diano4ka-milaya [45]
Answer is 120
AngNPQ=2*angNRQ=120
7 0
3 years ago
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