De Moivre's formula

There are two distinct complex numbers z, such that z³ is equal to 1 and z is not equal to 1.

Calculate the sum of these two numbers.

Correct answer:

S =  -1

Step-by-step explanation:

$$\begin{gathered} z^3=1 \\ 1=1(\cos 0+i\sin 0) \\ {z}_k=\sqrt[3]{1}(\cos ({\displaystyle \frac{2\pi k}{3}})+i\sin ({\displaystyle \frac{2\pi k}{3}})) \\ {z}_1=1 \\ {z}_2=\cos (120\mathrm{°})+i\sin (120\mathrm{°})=-0.5+0.866025403784i \\ {z}_3=\cos (240\mathrm{°})+i\sin (240\mathrm{°})=-0.5-0.866025403784i \\ S=z_2+z_3=-1 \end{gathered}$$

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