Re(cos(z)) on [-τ,τ]²

The real component of cosine on the complex rectangle going from -Ï„ (-2Ï€) to Ï„ (2Ï€) on each side.

Notice that if you take a slice down Im(z) = 0, you get your normal cosine function, and slices Im(z) = τn | n ∈ ℕ get you cosh.

(To understand what is going on, recall that cos(x) = ½(e^(iθ) + e^(-iθ)), because the two exponentials, moving on the unit circle, have their imaginary components cancel but the real combine, giving twice the real component, cos(x). When you give a compl