Question

So I tried to check Euler’s İdentity in python console:

import math
import cmath
cmath.exp(1j*math.pi)

and result was:

-1+1.2246063538223773e-16j

Shouldn’t it be just -1.

Answer 1

Imagine you were doing this calculation but you started with only 5 digits of pi and then at every stage you rounded to 5 significant figures. Do you think you’d get an exact answer? No, of course not, the tiny errors at each stage would produce an error in the answer.

Floating point maths is the same, except that this time you’re working in binary instead of decimal.