Find all roots of the equations (a) z^4 + 2z^2 + 4 = 0 My step: Let u = z^2 u^2 + 2u + 4 = 0 u = -1 + (3)^1/2 and u = -1 - (3)^1/2 i'm stuck at there...and tomorrow having complex number exam.
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Originally Posted by wkn0524 Find all roots of the equations (a) z^4 + 2z^2 + 4 = 0 My step: Let u = z^2 u^2 + 2u + 4 = 0 u = -1 + (3)^1/2 and u = -1 - (3)^1/2 i'm stuck at there...and tomorrow having complex number exam. Well, first your values for u are wrong. and . You forgot the "i". Now use the fact that . so so . I presume you will want to use d'Moivre's formula to take those square roots. Since and , in polar form, and .
Originally Posted by HallsofIvy Well, first your values for u are wrong. and . You forgot the "i". Now use the fact that . so so . I presume you will want to use d'Moivre's formula to take those square roots. Since and , in polar form, and . I forgot put i, its mean -1. there are four solution.
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