How do you find all the real and complex roots of $z^{5} = 1$ $z^5 =1$ ?

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Answer 1 · 2016-01-09T20:01:09

Real :

$z_{0} = 1$ $z_0 = 1$

Complex :

$z_{1} = - e^{\frac{π i}{5}}$ $z_1 = -e^((pii)/5)$

$z_{2} = e^{\frac{2 π i}{5}}$ $z_2 = e^((2pii)/5)$

$z_{3} = - e^{\frac{3 π i}{5}}$ $z_3 = -e^((3pii)/5)$

$z_{4} = e^{\frac{4 π i}{5}}$ $z_4 = e^((4pii)/5)$

How do you find all the real and complex roots of z^5 =1z5=1z^5 =1?