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Home Q & A Board Science-Related Homework Help Mathematics
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Smoren Smoren
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11 years ago
How do you solve the equation z^3=2, probably using complex numbers?
in other words, the solution might include complex numbers...

Please give a complete solution (including the method!).
Thanks!
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wrote...
#1
11 years ago
z^3 = 2
(z^3)^(1/3) = 2^(1/3)
z = 2^(1/3)
z = 1.25992, or 2^1/3
wrote...
#2
11 years ago
z = cuberoot(2)
z = 1.25992105
wrote...
#3
11 years ago
A simple way,
z^3 - [2^(1/3)]^3 = 0
=> [z - 2^(1/3)][z^2 - 2^(1/3)z + 2^(2/3)] = 0
z = 2^(1/3) = 1.2599, real solution
z = .6300 ± 1.0911 i, complex solution, obtained with quadratic formula.
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