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Asish Mahapatra Grade: 12th pass
        

Find real part of z=tan(a+ib)

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear ashish


z=tan(a+ib)


  let z = x+iy


so 


 x+iy = tan(a+ib)


x-iy = tan (a-ib)


add


 2x = tan(a+ib)  + tan (a-ib)


       =sin ( a+ib+a -ib)/2cos(a+ib)cos(a-ib)


       = sin2a / (cos2a + cos2ib)


      = sin2a/(cos2a + cosh2b)


x = sin2a/2(cos2a + cosh2b) 


 


 in above derivation we use cosi2b = cosh2b


  this a formula  and cosh2b is a real value,not imaginarry


  coshx =(ex + e-x )/2


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Badiuddin

7 years ago
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