What does sin(z with a hat) mean?

[laura_a]

Homework Statement

Sorry for the non-technical term, but I need to use cauchy-riemann equations on sin(z hat) and cos(z hat) to prove they're not analytic... which I'm sure I could try if I knew what it mean... I know for elementary maths that it means conjugate... but I can't find anywhere in my textbook which one to conj? If that's even what it is...

Homework Equations

sin(z) = [e^(iz) - e^(-iz) ] /2i

The Attempt at a Solution

so if that's the equation they want me to differentiate for C-R eqns then what is it's "hat" :) ...

 

[Dick]

"hat" of a+bi is a-bi. It's the complex conjugate, as you said.

 

[m2003]

I cannot provide a specific response without knowing the context in which "sin(z with a hat)" is being used. However, in general, the notation "z hat" could refer to the conjugate of the complex number z, denoted as z*. This means taking the complex conjugate of both the real and imaginary parts of z. For example, if z = a + bi, then z* = a - bi.

If this is the case, then sin(z with a hat) would mean taking the sine of the conjugate of z, which can be written as sin(z*) or sin(a - bi). In terms of the Cauchy-Riemann equations, this would involve differentiating the real and imaginary parts of sin(z*) separately and checking if they satisfy the equations.

However, without further context or clarification, it is difficult to determine the exact meaning of "sin(z with a hat)". It is important to carefully define notation and terminology in mathematics in order to avoid confusion.