How do you find the 4rd root of $81 e^{60 i}$ $81e^(60i)$ ?

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How do you find the 4rd root of $81 e^{60 i}$ $81e^(60i)$ ?

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Answer 1 · 2016-11-10T12:09:43

$3 e^{i (15 + k \frac{π}{2})}$ $3e^(i(15+kpi/2))$

Four roots each for k=0,1,2,3

Explanation:

$z^{4} = 81 e^{i (60 + 2 k π)}$ $z^4=81e^(i(60+2kpi))$
$z = \sqrt[4]{81} e^{i \frac{60 + 2 k π}{4}} = 3 e^{i (15 + k \frac{π}{2})}$ $z=root4(81)e^(i(60+2kpi)/4)=3e^(i(15+kpi/2))$

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How do you find the 4rd root of $81 e^{60 i}$ $81e^(60i)$ ?

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How do you find the 4rd root of 81e^(60i)81e60i81e^(60i)?

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How do you find the 4rd root of $81 e^{60 i}$ $81e^(60i)$ ?