Finding Omega: Evaluating sin^(-1)(3) on the Complex Plane

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Homework Statement

if z= sin (omega) find an expression for omega as a function of z that can be used to evaluate all possible values of sin^(-1) (3). Plot these values on the complex plane

The Attempt at a Solution

z= sin (omega)
3= sin (omega)

I don't know how to proceed from here. Please help

 

[Ray Vickson]

Homework Statement

if z= sin (omega) find an expression for omega as a function of z that can be used to evaluate all possible values of sin^(-1) (3). Plot these values on the complex plane

The Attempt at a Solution

z= sin (omega)
3= sin (omega)

I don't know how to proceed from here. Please help

For any w (real or complex) we have sin(w) = (1/2)*[exp(i*w) - exp(-i*w)], where i = sqrt(-1).

RGV

 

[Strants]

Actually, I believe the identity is \sin x = \frac{-i(e^{ix} - e^{-ix})}{2}.

 

[HallsofIvy]

Or, equivalentlty,
\frac{e^{ix}- e^{-ix}}{2i}