Find all values for z (complex number) where
sin (z)=2.

Find a branch of log(2z^2+1) that is analytic at i (imaginary number) adn compute the derivative at i

Question

Find all values for z (complex number) where 
sin (z)=2.

Find a branch of log(2z^2+1) that is analytic at i (imaginary number) adn compute the derivative at i

experimentx · Answer

try sin(z) = (e^z - e^-z)/2i = 2
try to find the value of e^z ... this will be quadratic.

experimentx · Answer

find e^z from there and then solve for z taking logs.

anonymous · Answer

$$sinz=\sin(a+ib)=cosasinib+cosibsina=sinxcoshy+isinhycosx=2$$

anonymous · Answer

$$*=isinh(b)cos(a)+\cosh(b)\sin(a)$$

anonymous · Answer

$$\sinh(b)\cos(a)=0$$
$$\cosh(b)\sin(a)=2$$

anonymous · Answer

Where these multivalued  functions intersect is your allowable values for a and b.

anonymous · Answer

Thank you for this