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

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

[John Doe]

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

[Mohammad Mahmudul Hasan]

5 rad = -1.2832 rad ?? you mean -1.2832 degree ?? but 5 radians = 286.478 degrees, i think.. or please tell me how do i get the 5 back.

[John Doe]

No, I meant what I said. If you want 5 back, you need to add 2*n*pi, where n is an integer (in this case 1). Why would you want an angle that is more than 2*pi? That's the equivalent of an angle larger than 360 degrees.

If you absolutely need the number you used in the exponential function, I recommend you save it as a variable, and use that variable later in your work.

x = 5;
z = exp(1i*x);

[Mohammad Mahmudul Hasan]

yeah, you are right it's y/x not the other way around. thanks you for help.

[John Doe]

If the answer provided is sufficient, please accept it. If not, explain what parts are not clear, and you will get additional help (from me or others). =)

[Mohammad Mahmudul Hasan]

thank you, for your reply, and as you've mentioned .. that i could save this variable to use later, but i will actually send this variable as a signal of "exp(1j*x)" to the receiver and receiver will extract 5 from this. So, i can't actually save it as a variable.

anyway, what i understood is this

>> angle(exp(1j*5)) +2*pi

ans =

     5

>> angle(exp(1j*4)) +2*pi

ans =

    4.0000

It works here but, when i go for 1 or 2...

>> angle(exp(1j*2)) +2*pi

ans =

    8.2832

>> angle(exp(1j*1)) +2*pi

ans =

    7.2832

shouldn't this be 1 and 2, as it worked for 4 and 5 ??

[John Doe]

No. Valid angles are in the area (-pi < x < pi). Since 4 and 5 are outside this area, the angles are not 4 and 5 (but -1.283.. etc). However, 1 and 2 are within the valid area, thus the angle is equal to 1 and 2 (without adding any +/-k*2*pi).