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Grade 11Algebra

When we have to find roots of z^3= -8
Do we convert -8 into +8? Please provide an explanation and solution.

Profile image of Gggggg
9 Years agoGrade 11
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1 Answer

Profile image of Vaibhav Singh
9 Years ago
z3 = -8
=> z3  = (-2)3
=> (-z/2)3 = 1
=> -z/2 = 1, \omega\omega2   ( Cube root of unity)
=> z = -2, -2\omega, -2\omega2 ( \omega =(-1 +\sqrt{}3i)/2 and  \omega2 =(-1 -\sqrt{}3i)/2 )
=> z = -2, 1 +\sqrt{}3i, 1 -\sqrt{}3i