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taurus [48]
2 years ago
12

Please give me the answer ASAP.

Mathematics
1 answer:
wel2 years ago
7 0

Answer:

-t+2>10

Step-by-step explanation:

Just ask.

Hope this helps! :D

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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
Determine la pendiente (m) de la recta que pasa por los puntos (2,3) y (- 2, - 4
labwork [276]
La pendiente de la recta que pasa por los puntos (2,3) y (-2,-4) es 7/4.

(2,3)      (-2,-4)
x₁ y₁       x₂  y₂

                y₂ - y₁       -4 -3           -7            7
              ----------- = --------- = ----------- = ------
                x₂ - x₁      -2 - 2           -4            4
                    ↑

                    ↑
la fórmula de el pendiente





5 0
4 years ago
Please help me with number 9-10
Finger [1]
(10). 423,,,,,,,,,,4.10=40.. Hopefully that's help u
7 0
3 years ago
I need help please if you TRULY know this NO LINKS!!!
Tcecarenko [31]

Answer:

ok post the question

Step-by-step explanation:

3 0
2 years ago
What is a unique fraction whose decimal form repeats? ( give a fraction that decimal repeats)
kramer

Answer:

1/9   0.1111

Step-by-step explanation:

1/9 = 0.11111111111....

6 0
3 years ago
Read 2 more answers
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