MATLAB: Please tell me what’s wrong here with the exp (1j*theta)

Question

I am trying to find the theta part from an exponential value.

Suppose, i take a variable

z=exp(1i*5);

so this will give me

z =

   0.2837 - 0.9589i

Now i want to find that "5" from this value. So, i go with this "angle(z)" and matlab shows

ans =

   -1.2832

Shouldn't it be 5, according to theory ??

Or if i go with the eular formula like, exp(i*theta)= cos(theta) + i*sin(theta)

so, theta= atan(0.2837/-0.9589) = -0.2877 !!

How do i get the theta=5 back, i don't know if i am missing something.

Answer 1

The reason is that:

5 rad = -1.2832 rad  % (-1.2832 + 2*pi = 5)

That is:

x = x + n*2*pi; % where x is an angle in radians, and n is an integer.

Matlab will always give you values between +/- pi.

And you use Eular the wrong way around: tan = sin/cos, not cos/sin.

=)

- Rob