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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

Thank you for this