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maria5633
13.06.2020 •
Mathematics
Z^5=-243i, find the solution to the equation whose argument is strictly between 180 degrees and 270 degrees. Round your answer to the nearest 10th
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Ответ:
The solution is
.
Step-by-step explanation:
Complex power is determined by means of the De Moivre's Theorem, whose expression is:
Where
is the norm of the complex number. In this case, expression can be written as:
The real component must be equal to zero and complex component must be equal to -1. That is to say:
Possible solutions for each component are, respectively:
Real component
Possible solutions:
,
, ![\frac{3\pi}{2}](/tpl/images/0684/8865/234a0.png)
Complex component
Possible solutions:
, ![\frac{3\pi}{2}](/tpl/images/0684/8865/234a0.png)
There is one solution whose argument is strictly between 180 degrees (
) and 270 degrees (
).
Ответ: