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de Moivre worked out a brilliant and beautiful way to solve complex equations.

If you for example have **z ^{3}= 1 **and you want to find all real and complex z that satisfy this equation. i is just a complex number written in rectangular form;

Rewrite i in euler form **1 = e ^{i * (0 + 2nπ) }= z^{3}**. Now, if we take the cube root of both sides, that will be the same as taking it to the power of 1/3.

Remember your __power rules__: (a^{b})^{c }= a^{b * c}. This will give you **z = e ^{i(0+n2π)/3}**. This is where the

**z _{0 }= 1** ;

Hope it helped. If not, well take it in the session