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Lunna [17]
4 years ago
11

Explain how to use scientific notation to solve

Mathematics
1 answer:
vesna_86 [32]4 years ago
6 0

Answer: 3

I just divided those two number and I got 3 also

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Suppose z = . What is z4?<br><br> on EDGE 2020
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Answer:

z^{4} = \cos \frac{8\pi}{3}+i\,\sin \frac{8\pi}{3}

Step-by-step explanation:

We can determine the power of a complex number by the De Moivre's Theorem, which states that for all z = r\cdot (\cos \theta + i\,\sin\theta), where a, b \in \mathbb{R}, the power of the complex number is:

z^{n} = r^{n}\cdot (\cos n\theta + i\,\sin n\theta) (1)

Where:

r - Magnitude of the complex number, dimensionless.

\theta - Direction of the complex number.

If we know that r = 1, n = 4 and \theta = \frac{2\pi}{3}, then the fourth power of the complex number is:

z^{4} = 1^{4}\cdot \left[\cos\left(\frac{8\pi}{3} \right)+i\,\sin\left(\frac{8\pi}{3}\right)\right]

z^{4} = \cos \frac{8\pi}{3}+i\,\sin \frac{8\pi}{3}

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Step-by-step explanation:

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