#let bgBlock(body, fill: color, width: 100%) = block(body, fill:fill.lighten(80%), width: width, inset: (bottom: 2mm))

#let SeperatorLine = line(length: 100%, stroke: (paint: black, thickness: 0.3mm))
#let MathAlignLeft(e) = {
  align(left, block(e))
}

#let subHeading(body, fill: color) = {
  box(
    align(
      top+center,
      text(
        body,
        size: 8pt,
        weight: "bold",
        style: "italic",
      )
    ),
    fill: fill,
    width: 100%,
    inset: 1mm,
    height: auto
  )
}

#let MathAlignLeft(e) = {
  align(left, block(e))
}

#let tableFillHigh = white
#let tableFillLow = color.lighten(gray, 50%)

#let sinTable = [
  #let data = json("../sintable.json")
  #table(
    columns: data.len(),
    rows: data.keys().len(),
    stroke: none,
    table.hline(stroke: (thickness: 0.3mm)),
    fill: (x, y) => if (calc.rem(y, 2) == 0) { tableFillLow } else { tableFillHigh },

    table.vline(),
    ..for (i, label) in data.keys().enumerate() {
      ([*#eval(label, mode: "math")*], if i > 0 { table.vline() } else { table.vline(stroke: none) })
    },

    table.hline(stroke: (thickness: 0.3mm)),
  
    ..for (i, v) in data.at("x").enumerate() {
    for (col) in data.keys() {
        (eval(data.at(col).at(i), mode: "math"),)
      }
    },
    table.hline(stroke: (thickness: 0.3mm)),
  )
]

#let ComplexNumbersSection(i: $i$) = [
  $1/#i = #i^(-1) = -#i quad quad #i^2=-1 quad quad sqrt(#i) = 1/sqrt(2) + 1/sqrt(2)#i$

  $z in CC = a + b #i quad quad quad z = r dot e^(phi #i)$ \
  $z_0 + z_1 = (a_0 + a_1) + (b_0 + b_1) #i$\
  $z_0 dot z_1 = (a_1 a_2 - b_1 b_2) + #i (a_1b_2 + a_2 b_1) = r_0 r_1 e^(#i (phi_0 + phi_1))$\
  $z^x = r^x dot e^(phi #i dot x) quad x in RR$ \
  $z_0/z_1 = r_0/r_1 e^(#i (phi_0 - phi_1)) quad quad quad$

  $r = abs(z) quad phi = cases(
    + arccos(a/r) space : space b >= 0,
    - arccos(a/r) space : space b < 0,
  )$
]