Exponential of Sum/Complex Numbers/Corollary

Corollary to Exponent of Sum: Complex Numbers
Let $z_1, z_2 \in \C$ be complex numbers.

Let $\exp z$ be the exponential of $z$.

Then:
 * $\exp \left({z_1 - z_2}\right) = \dfrac {\exp z_1} {\exp z_2}$

Proof
By Exponent of Sum: Complex Numbers:


 * $\exp \left({z_1 - z_2}\right) = \exp z_1 \exp \left({- z_2}\right)$

By Reciprocal of Complex Exponential:


 * $\dfrac 1 {\exp z_2} = \exp \left({- z_2}\right)$

Combining these two, we obtain the result:


 * $\exp \left({z_1 - z_2}\right) = \dfrac {\exp z_1} {\exp z_2}$