Question

solve the equation: (z^3)-1=0

Answer 1

\[z ^{3}-1=0\]

Answer 2

1

Answer 3

including imaginary roots

Answer 4

cube roots of 1 are what you want

Answer 5

\[\large z=1~~~z=\sqrt[3]{-1} ~~~ z=(-1)^{2/3}\]

Answer 6

1 is one of them others are taken by dividing up the unit circle in to 3 equal parts
you will get
\[-\frac{1}{2}+\frac{\sqrt{3}}{2}i\] and its conjugate

Answer 7

before we got reset, i tried to write solve
\[(z-1)(z^2+z+1)=0\] quadratic formula will give the second two solutions