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March 16th, 2017, 11:03 PM   #1
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Find all the complex solutions of the equation

(x^4) - 16 i = 0

Answers' to this question are supposed to be written in the following format:
r[cos(degree)+i sin(degree)] . . .

(i.e. We aren't solving for x)

Last edited by mymathforumuser; March 16th, 2017 at 11:28 PM.
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March 16th, 2017, 11:14 PM   #2
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$x^4 - 16 i = 0$

$x^4 = 16 i$

$x = 2 (i)^{1/4}$

$i = e^{i \pi/2}$

$(i)^{1/4} = e^{\frac{i \pi/2 + 2k\pi}{4}},~k=0,1,2,3$

$(i)^{1/4} = e^{i\pi/8}, e^{i5\pi/8}, e^{i9\pi/8}, e^{i13\pi/8}$

$x = 2e^{i\pi/8}, 2e^{i5\pi/8}, 2e^{i9\pi/8}, 2e^{i13\pi/8}$
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