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# Help ASAP pls

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There are four different fourth roots of 16. That is, there are four complex numbers that can be x in the equation below:

x^4=16

What are the four complex numbers?

Sep 25, 2019
edited by Guest  Sep 25, 2019

#1
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$$16 = 16 e^{i 2\pi k},~k \in \mathbb{Z}\\ \sqrt[4]{16} = \sqrt[4]{16}e^{i \frac{2\pi k }{4}},~k = 0, 1, 2, 3 = \\ 2e^{0},~2e^{i\pi/2},~2e^{i\pi},~2e^{i3\pi/2} = \\ 2, 2i, -2, -2i$$

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Sep 25, 2019

#1
+6045
+1

$$16 = 16 e^{i 2\pi k},~k \in \mathbb{Z}\\ \sqrt[4]{16} = \sqrt[4]{16}e^{i \frac{2\pi k }{4}},~k = 0, 1, 2, 3 = \\ 2e^{0},~2e^{i\pi/2},~2e^{i\pi},~2e^{i3\pi/2} = \\ 2, 2i, -2, -2i$$

Rom Sep 25, 2019
#2
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I haven't learned this yet, so just curious, how would 2 be considered to be a complex number?

CalculatorUser  Sep 26, 2019
#3
+6045
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All reals are also complex numbers.

A complex number need not have an imaginary part.

Rom  Sep 26, 2019