Can I plot complex function and how?

Question

pleas help me i need to plot sin(z) in Graphing Calculator 3D. Iam sorey for my bad english can i wrote w=sin(z) ? and get nothing

Answer 1

You can't do that, since the graph of $\sin$ is a subset of $\mathbb C^2=\mathbb R^4$.

But you use the fact that$$\sin(x+yi)=\sin(x)\cosh(y)+\cos(x)\sinh(y)i.$$The, you can graph:

• the real part of $\sin(z)$, which is $\sin(x)\cosh(y)$;
• the imaginary part of $\sin(z)$, which is $\cos(x)\sinh(y)$;
• the absolute value of $\sin(z)$, which is $\sqrt{\bigl(\sin(x)\cosh(y)\bigr)^2+\bigl(\cos(x)\sinh(y)\bigr)^2}$.