Third roots

Determine the sum of the three complex third roots of the number 64 .

Correct answer:

x =  0

Step-by-step explanation:

Φ=2π/3=2⋅ 3.1416/3≐2.0944 rad x1​=364​=4 y1​=0  x2​=x1​⋅ cos(Φ)=4⋅ cos2.0944=−2 y2​=x1​⋅ sin(Φ)=4⋅ sin2.0944=2 3​≐3.4641  x3​=x1​⋅ cos(2⋅ Φ)=4⋅ cos(2⋅ 2.0944)=−2 y3​=x1​⋅ sin(2⋅ Φ)=4⋅ sin(2⋅ 2.0944)=−2 3​≐−3.4641  x=x1​+x2​+x3​=4+(−2)+(−2)=0 y=y1​+y2​+y3​=0+3.4641+(−3.4641)=0

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