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I am an electronics undergraduate student currently learning wavelets. In the book A First Course in Wavelets with Fourier Analysis authors first introduce complex vectors and their dot products. Then they propose some properties of dot product on complex valued vectors. I understood the properties they given with some algebraic manipulation on formulas they provided (and I understood).

I always looked at the dot product (also 2D kernel convolutions and function correlations) as similarity queries between two given information. So, naturally, I asked "When everything was real, result of the dot product was a number and its positivity was giving me how similar were operand data. If components are not just numbers but arrows(I always thought complex numbers as arrows, never as a + bi), how would that similarity query result? Moreover, what does that mean for similarity of two vectors to be something complex or -as beloved James Grime says- compound?"

So, what did I do? I pondered, I imagined and this idea came out: Complex Vector Visualizer

I want to understand visually how dotting two arrow valued vectors behaves.

So, what is the reason of this post? It is for taking your advice. What do you think, what would you suggest me to learn or add to this so called visualizer? I am open to every constructive feedback.

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