Complex Algebra for Physics

Transcript

algebra is where we essentially create a placeholder number I which we Define to be the square root of1 which causes the core principle of it to be that it square is minus one so for example this might come up in quadratics where the discriminant is negative so we get this formula pretty beautiful Oiler identity which stems from the tailor expansion of cosine sin of X where is this useful well an oscillatory system it turns out that while cosine and S are good solutions to these kinds of linear differential equations e to the x is also a good solution too which means when we get an imaginary number out of this solution then we're actually able to simplify it into a trigonometric function as per Oiler identity so that's complex algebra and how it's useful in physics