De Moivre's formula

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

Calculate the sum of these two numbers.

Correct result:

S =  -1

Solution:

z3=1 1=1(cos⁡0+isin⁡0) zk=13(cos⁡(2πk3)+isin⁡(2πk3)) z1=1 z2=cos⁡(120∘)+isin⁡(120∘)=−0.5+0.866025403784i z3=cos⁡(240∘)+isin⁡(240∘)=−0.5−0.866025403784i S=z2+z3=−1

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