How Do You Convert sin^2(z) into x+iy Form?

[jjangub]

Homework Statement

How do I change sin^2(z) to x+iy form? (z=x+iy)
I have to put this x and y to arctan(y/x)

Homework Equations

The Attempt at a Solution

I tried to use sin^2(z) = 1/2 -1/2(cos(2z)) or sin(z) = ((e^(iz) - e^(-iz))/2i)^2
but both ways I cannot take out i.
Or isn't the sin only takes the imagenary part? so there is no x and only y exists.
It brings us that artan(0) = 0?
I am confused about these cases like when there is sin(z) and cos(z)...
Thank you.

 

[Outlined]

z is real?

 

[Winzer]

How would you expand Sin(x + i y)?
Using a trig identity.

 

[Liquidxlax]

Homework Statement

How do I change sin^2(z) to x+iy form? (z=x+iy)
I have to put this x and y to arctan(y/x)

Homework Equations

The Attempt at a Solution

I tried to use sin^2(z) = 1/2 -1/2(cos(2z)) or sin(z) = ((e^(iz) - e^(-iz))/2i)^2
but both ways I cannot take out i.
Or isn't the sin only takes the imagenary part? so there is no x and only y exists.
It brings us that artan(0) = 0?
I am confused about these cases like when there is sin(z) and cos(z)...
Thank you.

that's not how it works