[問卦] 突然想到奇怪的根號問題

剛剛不小心想到指數問題 百思不得其解

(-2)^5 = -32 => -2 = (-32)^(1/5)

所以(-32)^(1/5) = -2 ...(1)

又 r*Exp[i*theta] = (-32) = 32*(-1) ...r = 32, theta = Pi

=> (-32)^(1/5) = r^(1/5) * (Exp[i*theta])^(1/5) ...polar form

= (32)^(1/5) * (Exp[i*Pi])^(1/5)

= 2*Exp[i*Pi/5]

= 2*(Cos[Pi/5]+i*Sin[Pi/5]) ...(2)

有沒有為什麼(1)!=(2)的八卦?

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