When I calculate exp(3.8566e5*1i) and exp(data*1i) answers are different why? Here, data=3.8566e5

>> Data

Data =

3.8566e+005

>> exp(1i*3.8566e5)

ans =

   0.6076 + 0.7942i

>> exp(1i*Data)

ans =

   1.0000 - 0.0000i

>>

Answer 1

[Roger Stafford]

When you display 'Data' with

   Data =

   3.8566e+005

the difference between the actual value of 'Data' and the displayed value due to rounding off in "format short" could be as large as .00005e+005 = 5 radians = 286 degrees, and that would completely alter the value of exp(Data*i) = cos(Data)+i*sin(Data). This is in addition to the discrepancy noted by Azzi.

[Prajan Pradhan]

 Data

Data =

3.8566e+005

>> exp(Data*1i)

ans =

   1.0000 - 0.0000i

>> exp(3.8566e+005*1i)

ans =

-0.3367 - 0.9416i

Now what do you say? I mistakenly left one digit after decimal.

[Roger Stafford]

Here is what I say, Prajan. Very likely you are using "format short" by default and you probably set 'Data' to:

   Data = 61380*2*pi;

Then you displayed Data and got

   Data = 
   3.8566e+05

Then you displayed both exp(Data*i) and exp(3.8566e+05*i) and got:

   ans =  
   1.0000 - 0.0000i

   exp(3.8566e+05*i) = 
   -0.3367 - 0.9416i

However, if you had displayed Data more accurately, say using "format long", you would have got:

   format long
   Data =
   3.856619141546830e+05

Then if you display exp(Data*i) and exp(3.856619141546830e+05*i), you will get:

   ans = 
   1.00000000000000 - 0.00000000001103i

   ans =
   1.00000000000000 - 0.00000000001103i

Your problem was in evaluating exp for two different quantities. You thought they were the same because you were depending on the default and not very accurate "format short" for displaying them, but they were actually significantly different.

[Prajan Pradhan]

thank you!

Answer 2

[Azzi Abdelmalek]

Why are yoy surprised? you are using two different numbers (3.8566 and 3.856). try this

Data =3.8566e+005
exp(1i*3.8566e5)
exp(1i*Data)

[Prajan Pradhan]

 Data

Data =

3.8566e+005

>> exp(Data*1i)

ans =

   1.0000 - 0.0000i

>> exp(3.8566e+005*1i)

ans =

-0.3367 - 0.9416i

Now what do you say? I mistakenly left one digit after decimal.