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⋅ 3.1416​≐1.2566 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)≐1.0036⋅10−13  s=x+i⋅ y s=0

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