Exponential function: Difference between revisions

Revision as of 13:14, 1 April 2003

Revision as of 06:03, 5 May 2003

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: <math>\exp(a + bi) = \exp(a) \cdot (\cos(b) + i * \sin(b))</math>

where <math>a</math> and <math>b</math> are real values. This formula connects the exponential function with the [[trigonometric function]]s, and this is the reason that extending the natural logarithm to complex arguments naturally yields a multi-valued function ln(''z''). We can define a more general exponentiation:

: <math>z^w = \exp(\ln(z) w)</math>

for all complex numbers ''z'' and ''w''.