vspace

Author: pavelkomarov

doc/math.tex

@@ -58,13 +58,13 @@ \subsection{The Fourier Basis}\label{fourierB}
 
 Lo and behold, the famous transfer function [contains] exactly the eigenvalues of the corresponding eigenfunctions! Upon asking various electrical engineers what the transfer function was, no one has ever told me that! Yes, when pointed out to them that it is the same idea they have to agree, but the fact it is the same idea never seemed to have crossed their minds! The same, simple idea, in two or more different disguises in their minds, and they knew of no connection between them! Get down to the basics every time!"\end{quotation}
 
-In that spirit, with Patron Saint Hamming watching over us, let's continue: \autoref{fourierB}}, which is the set of complex exponentials:
+In that spirit, with Patron Saint Hamming watching over us, let's continue: \autoref{fourierB}}, which is the set of complex exponentials:\vspace{-2mm}
 
 \begin{equation}\label{euler}
 e^{j \omega} = \cos(\omega) + j \sin(\omega)
 \end{equation}
 
-where I use $j$ to represent the imaginary unit, because I'm from Electrical Engineering, and because Python uses \texttt{j}.\newline
+where I use $j$ to represent the imaginary unit ($\sqrt{-1}$), because I'm from Electrical Engineering, and because Python uses \texttt{j}.\newline
 
 Why this identity is true isn't obvious at first but can be seen by \href{https://math.stackexchange.com/a/492165/278341}{Taylor Expanding}\cite{taylor} the exponential function and trigonometric functions: