Saturday, 28 May 2016

multivariable calculus - What are the real and imaginary parts of the complex function?




So, it is asked to find the real and imaginary parts of the specific complex function:



f(z)=sin(z)+i(3z+2)
So I use z as z=x+iy



everything seemed clear till I met Mr. Sinus:



u+iv=sin(x+iy)+i(3(x+iy)+2)




and I don't really know how to seperate the imaginary and real parts of sin(x+iy) argument.



Need hints...


Answer



Hint:



use addition formula: sin(x+iy)=sinxcos(iy)+cosxsin(iy) and remember that: cos(iy)=cosh(y) and sin(iy)=isinhy.


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