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: <math>e^{a + bi} = e^a (\cos b + i \sin b)</math>
where <i>a</i> and <i>b</i> are real values. This formula connects the exponential function with the [[Trigonometric function|trigonometric functions]], and this is the reason that extending the natural logarithm to complex arguments yields a [[multi-valued function]] ln(<i>z</i>). We can define a more general exponentiation:
: <math>z^w = e^{w \ln z}</math>
for all complex numbers <i>z</i> and <i>w</i>.
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