A little complex number test

main.lua

local CX, CY = display.contentCenterX, display.contentCenterY

local N = 15
local R = 50

local cosa, sina = R, 0 -- can be R, 0 if you have a fixed radius; otherwise, you will scale these
                        -- intermediate steps

local cosda, sinda = math.cos(2 * math.pi / N), math.sin(2 * math.pi / N)

-- https://math.stackexchange.com/questions/465070/multiplying-two-complex-numbers-using-only-three-multiplications-of-real-numbers
-- a = cos(A), b = sin(A), c = cos(dA), d = sin(dA)
-- P1 = ac, P2 = bd, P3 = (a + b)(c + d)
local c_plus_d = cosda + sinda

for i = 1, N do
  -- do something with (cosa, sina)
  local cc = display.newCircle(CX + cosa, CY + sina, 5)

  cc:setFillColor(0, 0, 1)

  -- Rotate by angle delta.
  local P1, P2, P3 = cosa * cosda, sina * sinda, (cosa + sina) * c_plus_d

  cosa, sina = P1 - P2, P3 - P2 - P1
end