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:

z3=1 1=1(cos0+isin0) zk=31(cos(32πk)+isin(32πk)) z1=1 z2=cos(120°)+isin(120°)=0.5+0.86602540378444i z3=cos(240°)+isin(240°)=0.50.86602540378444i S=z2+z3=1

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