5 pages
Complex numbers
Numbers as points in a plane, where multiplying means rotating. The arithmetic behind phase, spectra, and the FFT.
read it →
Decibels (dB)
How dB turns enormous loudness ratios into small, readable numbers, and why +6 dB means double.
read it →
Euler’s formula
Why e appears in a formula about circles, and why eⁱᶿ means “rotate by θ”. The spiral construction makes both visible.
read it →
Logarithms and exponents
The inverse of raising-to-a-power: why logs turn multiplication into addition, what log₂ counts, and how to read a log the way you read an exponent.
read it →
Parameterization and substitution
Two different moves hide inside “substitute and simplify”: composing with a new input, as in θ = 2πft, and extending a definition, as in eⁱᶿ. Which move is in play determines what stays true.
read it →