bug in power calcultion while in loop ?

So, I've been doing a project lately and I come upon this interesting bug.

here's a variable W which uses the euler's formula i.e., cos(2*pi*1i/8) +

W = cos(2*pi/8) + sin(2*pi/8);

or even the exponent form

W = exp(2*pi*1i/8);

Now, if i use a power k = 2 on this variable, I get the result as intended

>> k = 2
k =
     2
>> W^k

ans =
   0.0000 + 1.0000i

Here's the one in a loop in the command window which is fine again

   for k = 1:4
disp(W^(k-1));
end
     1

   0.7071 + 0.7071i

   0.0000 + 1.0000i

  -0.7071 + 0.7071i

but, when i put this in a loop inside my program this is the result

for k = 1:4
        g(k) = W^(k-1);
        disp("W^(k-1) " + W^(k-1));
       
end
W^(k-1) 1
W^(k-1) 0.70711+0.70711i
W^(k-1) 2.2204e-16+1i
W^(k-1) -0.70711+0.70711i

how did this bug occur such that it's working perfectly fine in commands but not in program ?

Answer 1

[Rik]

This is not a bug. Look at the exponent: 2e-16 is very small. It is close enough to eps that you can assume that is just 0.

The reason in the way computers store values. Just like you can't store the result of 1/3, computers can't store every number. If you can only store 4 decimals 3*(1/3) will be 0.9999, not 1.

[Aswin Prasanna Suriya Prakash]

I see.

But somehow I'm in the impression that this negligible number is completely ruining my final result. Is there any way to rectify this so the results of its iterations won't get affected also ?

[Rik]

You probably don't have to do anything, but you could round to some maximum precision.

Answer 2

[Image Analyst]

See the FAQ: https://matlab.fandom.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

and

https://matlab.fandom.com/wiki/FAQ#Does_MATLAB_only_calculate_to_4_significant_digits.3F

[Aswin Prasanna Suriya Prakash]

Thank you