De Moivre's formula

There are two distinct complex numbers, 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(cos 0 + i sin 0 ) zk​ = ( cos( 32 π k​ ) + i sin( 32 π k​ )) 1/3 z1​ = 1 z2​ = cos( 120° ) + i sin( 120° ) = −0.5 + 0.86602540378444 i z3​ = cos( 240° ) + i sin( 240° ) = −0.5 − 0.86602540378444 i  S = z2​ + z3​  S=−0.5+(−0.5)=−1

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