Complex sine function Sin ( pi + i Ln 3 ) Complex Analysis

Use Complex Analysis to calculate this crazy sin function .
First we have the double angle formula for sin . Sin (A+B) = sinAcosB + cosAsinB .
After we calculate sin(pi)=0 , cos(pi)=-1 .
Then we are left with a complex sin function identity . sin(iz) = i sinh z , where sinh z is the hyperbolic sine function .
Then we are finally left with the exponential identity for sinh . sinh(z) = 1/2(e^z-e^-z) .
The exponential rules gives the 2 inverse functions exp , Ln cancel each other
.
Other complex analysis questions are found here .

#algebra
#complex
#maths
#cauchy
#calc3
#calculus
#analysis
#mathematics