how do you find real and imaginary parts of cos(z)

Question : Find real and imaginary parts of cos(z) Solution :First we shall put \[z=x+iy\] then \[cos(z)=cos(x+iy)\]now using the formula of \[cos(A+B)=cos(A)cos(B)-sin(A)sin(B)\] we get \[cos(x+iy) = cos(x)cos(iy)-sin(x)sin(iy)\] now by the formulas \[cos(iy)=cosh(y) , sin(iy)=isinh(y)\] then we shall have \[cos(x+iy) =…

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