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 March 16th, 2017, 11:03 PM #1 Newbie   Joined: Mar 2017 From: home Posts: 2 Thanks: 0 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.
 March 16th, 2017, 11:14 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 1,944 Thanks: 1011 $x^4 - 16 i = 0$ $x^4 = 16 i$ $x = 2 (i)^{1/4}$ $i = e^{i \pi/2}$ $(i)^{1/4} = e^{\frac{i \pi/2 + 2k\pi}{4}},~k=0,1,2,3$ $(i)^{1/4} = e^{i\pi/8}, e^{i5\pi/8}, e^{i9\pi/8}, e^{i13\pi/8}$ $x = 2e^{i\pi/8}, 2e^{i5\pi/8}, 2e^{i9\pi/8}, 2e^{i13\pi/8}$ Thanks from topsquark and mymathforumuser

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