x-5-1-0-please-how-do-i-find-for-all-the-values-of-x-

Question Number 166241 by MathsFan last updated on 15/Feb/22

x^{5} - 1 = 0

p l e a s e h o w d o i f i n d f o r a l l t h e

v a l u e s o f x ?

Answered by batamatikayoga last updated on 16/Feb/22

x^{5} = 1 = e^{2 π i k}, k \in {1, 2, 3, 4, 5}

x = e^{\frac{2}{5} π i k}

Commented by MathsFan last updated on 16/Feb/22

1 + e^{π i} = 0

1 = - e^{π i} ? ? ? ?

Commented by alephzero last updated on 16/Feb/22

y e s

1 = - e^{i π}

\Rightarrow - 1 = - (- e^{i π}) = e^{i π}

Answered by JDamian last updated on 16/Feb/22

x = e^{\frac{2 π i}{5} k} \forall k \in {0, 1, 2, 3, 4}

Commented by MathsFan last updated on 16/Feb/22

t h a n k y o u s i r