# why the result not contain imaginary, I? [closed]

Good day,

First of all, sorry if my coding in this forum has mistake. I already learned it and this is the best try from me.

May anyone help me troubleshoot my problem below.

β1 = 0;
β3 = Pi;
β2 = Pi/2;
For[t = 0, t < 10, t++,
A={{E^(I β1 + I β3) Cos[t*β2],   E^(I β1 - I β3) Sin[t*β2]},
{(-E^((-I) β1 + I β3)) Sin[t*β2], E^((-I) β1 - I β3) Cos[t*β2]}};
Print[A];Print[t];t = t + TimeUsed[]]


I get the output as example as below,

{{1,0},{0,1}}

0

{{-0.740687,0.67185},{-0.67185,-0.740687}}

1.531

{{0.122216,-0.992504},{0.992504,0.122216}}

3.078

{{0.55557,0.83147},{-0.83147,0.55557}}

4.625

{{-0.963724,-0.266902},{0.266902,-0.963724}}

6.172

{{0.904157,-0.4272},{0.4272,0.904157}}

7.719

{{-0.40578,0.913971},{-0.913971,-0.40578}}

9.266


suppose the answer will include the symbol I. But what the mistake that I did.?

Thank you

Thank you for the @Edmund according to Euler Formula. I already read that and it correct output from the coding.

Since the Euler Formula is given by,

e^(ix)= Cosx+ iSinx.


where the x in angle rotating the plane.

Thank you

## closed as off-topic by MarcoB, george2079, Yves Klett, bbgodfrey, SumitJul 25 '16 at 14:54

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• I don't get your results. However, have a read of Euler's formula from complex analysis and you see that the $e^{i n x}$ are evaluating to either 1, 0, or -1 in your formulas. – Edmund Jul 25 '16 at 10:04
• @Edmund, I edit it for the output.when i calculate manually, the result suppose include I.why?. – munirah Jul 25 '16 at 11:30
• what is the logic behind incrementing t by timeused?? – george2079 Jul 25 '16 at 11:55
• @george2079, actually, I want to see the changes of the value when I increase the time by used time provided by computer system. From my reading, timeused is time given by computer. But why the I is not included in the output? – munirah Jul 25 '16 at 12:11
• I'm voting to close this question as off-topic because the problem seems to stem from a possible misunderstanding of the underlying math, and not from the code. – MarcoB Jul 25 '16 at 13:24

Table[{x, Exp[I x] // N}, {x, 0, Pi, Pi/2}] // TableForm

$\begin{array}{cc} 0 & 1. \\ \frac{\pi }{2} & 0.\, +1. i \\ \pi & -1. \\ \end{array}$