Notes: Classwork and Academia #
- Mathematics
- Mathematics #
- Electrical Engineering
- Electrical and Computer Engineering # Analytical Foundations Analytical Foundations of ECE # Complex Numbers # Definition of a Complex Number # Consider \(x^2-1=0\) . To find the roots: \[\begin{aligned} x^2-1 &= 0\\ x^2 &= 1\\ x &= \sqrt{1}\\ \rArr x &= \plusmn{1} \end{aligned}\] Now consider \(x^2+1=0\) : \[\begin{aligned} x^2 + 1 &= 0\\ x^2 &= -1\\ x &= \sqrt{-1}\\ \rArr x &= \plusmn{j} \end{aligned}\] \(j\) is an imaginary unit introduced to solve this type of equation.
- Physics
- Physics #