Question

I. Find the points at which w = cosh z is not conformal.

Answer 1

• The plate for the constant temperature on the line segment {w=u+iv : -1<u<1, v=0}
• To an outer boundary for the cooler constant temperature with a given by the ellipse u^2/cosh^2(1) + v^2/sinh^2(1) = 1

z=x+iy

cosh(z) = (e^z+e^-z)/2 = ... = cosh(x)cos(y) + i*sinh(x)sin(y)

Therefore equations for ellipse and hyperbola .

To increase the rectangle z-plane, it has the direction to recognize to transform for the lines through w=cosh(z) and similarly ellipses convert to vertical lines.