EXP function with imaginary number

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Nguyen Trung Kien 2018-9-3

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https://ww2.mathworks.cn/matlabcentral/answers/417247-exp-function-with-imaginary-number

评论： madhan ravi 2018-9-4

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.

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Stephen23 2018-9-3

编辑：Stephen23 2018-9-3

在 MATLAB Online 中打开

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 2018-9-4

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.

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