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 3.1416/32.0944 rad x1=364=4 y1=0  x2=x1 cos(Φ)=4 cos2.0944=2 y2=x1 sin(Φ)=4 sin2.0944=2 33.4641  x3=x1 cos(2 Φ)=4 cos(2 2.0944)=2 y3=x1 sin(2 Φ)=4 sin(2 2.0944)=2 33.4641  x=x1+x2+x3=4+(2)+(2)=0 y=y1+y2+y3=0+3.4641+(3.4641)=0



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