# Writing f(z) in its real and complex parts.

• December 12th 2010, 10:05 AM
snido757
Writing f(z) in its real and complex parts.
I need help rewriting f(z) as f(z)=u+iv. In particular I need help with sin(z^2) and sec(z).

I believe Sec(z) would just be Sec(x)Sech(y)+i(-Csc(x)Csch(y)). Or just the inverse of cos(z)

However I cannot find a way to relate Sin(z) to Sin(z^2).

• December 12th 2010, 10:21 AM
snowtea
If you know sin(z)

Why not just expand z^2 into real and imaginary parts, then it looks just like z' = (x^2 - y^2) + (2xy)i.

Can you find sin(z^2) = sin(z') now?
• December 12th 2010, 11:15 AM
Plato
$\sin(z^2)=\sin(x^2-y^2)\cosh(2xy)+i~\cos(x^2-y^2)\sinh(2xy)$