Question

How to solve complex number : x^3=i^3 for x € C

Answer 1

`x^3=i^3\\\\x^3-i^3=0\\\\(x-i)(x^2+xi-1)=0\\\\x=i\\\\\\\x^2+xi-1=0\\\\\Delta=i^2-4\cdot1\cdot(-1)=-1+4=3\\\\√(\Delta)=\sqrt3 \\\\x_1=(-i-\sqrt3)/(2)=-(\sqrt3)/(2)-(1)/(2)i\\\\x_2=(-i+\sqrt3)/(2)=(\sqrt3)/(2)-(1)/(2)i\\\\\\\boxed{x\in\left\{i,-(\sqrt3)/(2)-(1)/(2)i,(\sqrt3)/(2)-(1)/(2)i\right\}}`