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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.
=== Exponential function and differential equations ===
The exponential function solves the basic equation
dy
-- = y
dx
and for this reason is exponential function is frequently
encountered in differential equations. In particular
the solution of linear ordinary [[differential equation]]s
can frequently be written in terms of exponential functions.
These equations include [[Schrodinger's equation]] and the
[[Laplace equation]] as well as the equations for [[simple harmonic motion]].
=== Exponential function for matrices and Banach algebras ===
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