There is something very pleasing about _numerically_ calculating that e^iπ=-1.

(defn cadd [[xr xi] [yr yi]]

[(+ xr yr) (+ xi yi)])

(defn cmul [[xr xi] [yr yi]]

[(- (* xr yr) (* xi yi)) (+ (* yr xi) (* xr yi))])

(defn cscale [[xr xi] s]

[(/ xr s) (/ xi s)])

(defn cprn [[xr xi]]

(prn (double xr) '+ (double xi) 'i))

(defn compound [balance rate periods]

(let [period-rate (cadd [1 0] (cscale rate periods))]

(loop [balance [balance 0]

periods periods]

(if (zero? periods)

balance

(recur (cmul balance period-rate) (dec periods))))))

(cprn (compound 1 [0 3.141592653589793] 100000))

-1.0000493492396174 + 1.0335963488293152E-9 i