EXP function with imaginary number

I am working with Matlab to reproduce SAR image by radar. But when I calculate the EXP function, the result is so different.

>> exp(0.000000000000000e+00 - 8.378507193591911e+06i)
ans =
   0.5122 + 0.8588i

>> exp(0.000000000000000e+00 - 8.378522834360446e+06i)
ans =
  -0.4534 - 0.8913i

I do not know why in the result, one is negative, and one is positive. Please help me with this. Thank you so much for your consideration.

[Torsten]

exp(it) = cos(t)+i*sin(t)

So why are you surprised about the result ?

Best wishes

Torsten.

[Stephen23]

There is nothing surprising about those results, their difference is more than 2*pi:

>> L = 8.378507193591911e+06;
>> R = 8.378522834360446e+06;
>> R-L
ans =  15.641

You can plot this easily, and see how that range includes real and imaginary parts that are both positive and negative:

>> V = linspace(L,R,100);
>> E = exp(complex(0,V));
>> plot(E,'-*')

>> M = [real(E(:)),imag(E(:))];
>> plot(V,M,'-*')

[Nguyen Trung Kien]

Thank you so much for your comments. I understood that everything is normal and my question is weird so I had closed it. Many thanks for your explanations.

Answer 1

[madhan ravi]

I tried and got the same result too even the result in Wolfram is the same.

[Nguyen Trung Kien]

Because if I continue using this result for Fast Fourier Transform, the final result will become wrong. So do you have any suggestion for me in this situation?

[madhan ravi]

No there is nothing wrong with both the answers. You can also verify the results in other appilications they give the same answers as the above.Even if you paste the expressing in google the answers you get are the same!

[Nguyen Trung Kien]

I have just tried with excel, and same as your attention. Thank you so much. I think I will close this question.

[madhan ravi]

Your welcome and don’t close the question.