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human Secrets
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See § Actual exponents and § Non-integer powers of complex numbers for aspects on how these complications can be taken care of. Authentic exponents[edit]
these values are similar to All those described in § nth roots of a complex range. If w is an integer, there is just one worth that agrees with that of § Integer exponents.
Logarithm of z. The principal worth of this logarithm is log z = ln ρ + i θ , displaystyle log z=ln rho +itheta ,
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Raising 0 to some detrimental exponent is undefined but, in some situation, it could be interpreted as infinity ( ∞ displaystyle infty
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denotes one of several values in the multivalued logarithm (commonly its principal price), one other values are two i k π + log z , displaystyle 2ikpi +log z,
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The Restrict of the sequence of powers of the amount bigger than a single diverges; To put it differently, the sequence grows without sure:
英語-中文(繁體) phrase #beta Beta /beta #preferredDictionaries ^chosen identify /chosen /preferredDictionaries
The definition with the exponentiation being an iterated multiplication can be formalized through the use of induction,[20] and this definition can be utilized as soon a person has an associative multiplication:
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