Cotangent Exponential Formulation

Theorem
Let $z$ be a complex number such that $\forall k\in \Z$, $z \neq k \pi$:

Let $\cot z$ denote the cotangent function and $i$ denote the imaginary unit: $i^2 = -1$.

Then:
 * $\cot z = i \dfrac {e^{i z} + e^{-i z} } {e^{i z} - e^{-i z} }$

Also defined as
This result is sometimes also presented as:
 * $\cot z = \dfrac {i \paren {e^{i z} + e^{-i z} } } {e^{i z} - e^{-i z} }$

Also see

 * Sine Exponential Formulation
 * Cosine Exponential Formulation
 * Tangent Exponential Formulation
 * Secant Exponential Formulation
 * Cosecant Exponential Formulation


 * Arccotangent Logarithmic Formulation