Thursday, 25 September 2014

Modulus of complex number



|2eit1|2




I don't understand how to work this out, I know if I had for example |2ti1|2 then I would square the real and imaginary parts and add them to get the modulus squared, but here I have |2eit1|2 and I don't understand what to do.



Any help would be much appreciated.


Answer



Considering that t is real, we use Euler's formula eiθ=cosθ+isinθ



|2eit1|2=|2cost+2isint1|2=(2cost1)2+(2sint)2



This evaluates as (54cost) and as you can see, the value is dependent on t which is the argument of the complex number eit in polar form.


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