Fifth 3871

What is the sum of the fifth root of 243?

Correct answer:

s =  0

Step-by-step explanation:

a=5243=3 α=52π=52 3.14161.2566 rad  x1=a cos(0 α)=3 cos(0 1.2566)=3 x2=a cos(1 α)=3 cos(1 1.2566)0.9271 x3=a cos(2 α)=3 cos(2 1.2566)2.4271 x4=a cos(3 α)=3 cos(3 1.2566)2.4271 x5=a cos(4 α)=3 cos(4 1.2566)0.9271  x=x1+x2+x3+x4+x5=3+0.9271+(2.4271)+(2.4271)+0.9271=0  y1=a sin(0 α)=3 sin(0 1.2566)=0 y2=a sin(1 α)=3 sin(1 1.2566)2.8532 y3=a sin(2 α)=3 sin(2 1.2566)1.7634 y4=a sin(3 α)=3 sin(3 1.2566)1.7634 y5=a sin(4 α)=3 sin(4 1.2566)2.8532  y=y1+y2+y3+y4+y5=0+2.8532+1.7634+(1.7634)+(2.8532)1.00361013  s=x+i y s=0

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