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# I don't understand this, please explain and help!

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The number \(16\) has four fourth roots. In other words, there are four complex numbers that can be entered in the square in the equation below: \(\square^4=16.\) Find them.

I know that 2 is one, but I don't know how to find the others. Could anyone please provide an explanation with their answer? Thank you!

Jul 1, 2020

#1
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hi otterstar!

so we know that \((-2)^4=16\) since -2*-2*-2*-2=16

since there are 4 roots, and we've already covered all the real ones, we have to look for complex numbers now.

we also know that \(i^4=1\), so that means that \((2i)^4=16\) since 2^4 already equals 16, and multiplying it by 1 will equal 16 too.

lastly, we know that \((-2i)^4=16\)  since we already know that -2^4 equals 16 (as we found earlier) and multiplying it by i^4=1 will equal 16 too.

so the solutions are \(\boxed{2,-2,2i,-2i}\)

i hope this helped you! :)

Jul 1, 2020
#2
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Thank you so much!

Otterstar  Jul 1, 2020
#3
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no problem! :)