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Complex logartihmic spiral |
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for all complex numbers ''z'' and ''w''.
This is then also a multi-valued function. The above stated exponential laws remain true if interpreted properly as statements about multi-valued functions.
It is easy to see, that the exponential function maps any [[line]] in the complex plane to a [[logarithmic spiral]] in the complex plane with the centre at 0, noting that the case of a line parallel with the real or imaginary axis maps to a line or [[circle]].
=== Exponential function for matrices and Banach algebras ===
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