The precision of your exposition makes me more attentive to precision itself. So, when you say that the matrix for the imaginary part captures the coefficients (with the matrix multiplied by the scalar complex unit i), I want to describe the real part also as the "coefficients" of the real part (invisibly multiplied by the scalar real unit, 1) It helps me to use the word "coefficients" in both cases, ,because otherwise I want to put a "1" where actually the coefficient is 0 (for the real or imaginary part). I see 6i, and I want to make the real coefficient "1" rather than zero; it's a brain fart, but if I'm not thinking "coefficient" then I'm thinking something like "thing" and that makes me erroneously imagine a "1" has to go there; can't have an "empty" entry. #doh It's lapses like this on my part (or errors in my math training, to put it less self-pejoratively) that really weaken my facility with math and why I appreciate the pace and clarity of your exposition. I really require baby steps, and you aren't so eager to churn out content, or so bored at having to do such exposition, or not so clueless that you imagine just writing something on a screen constitutes demonstrating something to a learner; it actually takes an unusual degree of patience on your part (I imagine); at least, other math presenters can't manage to do it. So, again kudos to your successful pedagogy; I recall you said that was something you wanted to dedicate your life to, and you are doing an effective job of presenting the ideas.
![The most beautiful equation in math, explained visually [Euler’s Formula]](http://i.ytimg.com/vi/f8CXG7dS-D0/mqdefault.jpg)
The precision of your exposition makes me more attentive to precision itself. So, when you say that the matrix for the imaginary part captures the coefficients (with the matrix multiplied by the scalar complex unit i), I want to describe the real part also as the "coefficients" of the real part (invisibly multiplied by the scalar real unit, 1)
It helps me to use the word "coefficients" in both cases, ,because otherwise I want to put a "1" where actually the coefficient is 0 (for the real or imaginary part). I see 6i, and I want to make the real coefficient "1" rather than zero; it's a brain fart, but if I'm not thinking "coefficient" then I'm thinking something like "thing" and that makes me erroneously imagine a "1" has to go there; can't have an "empty" entry. #doh
It's lapses like this on my part (or errors in my math training, to put it less self-pejoratively) that really weaken my facility with math and why I appreciate the pace and clarity of your exposition. I really require baby steps, and you aren't so eager to churn out content, or so bored at having to do such exposition, or not so clueless that you imagine just writing something on a screen constitutes demonstrating something to a learner; it actually takes an unusual degree of patience on your part (I imagine); at least, other math presenters can't manage to do it. So, again kudos to your successful pedagogy; I recall you said that was something you wanted to dedicate your life to, and you are doing an effective job of presenting the ideas.