Hi everyone! I have a question about mathematical methods in physics. The question is Turkish in attached but I translated it for you. Can you help me please? Thx a lot. (a) Show that the function ω satisfies the condition ∇⃗ u ∙ ∇⃗ v = 0 so that the function is analytical (where ∇⃗ is the del operator and it is defined as ∇⃗ ∶ = î × ∂ / ∂x + î × ∂ / ∂y. U = î × ∂u / ∂x + î × ∂u / ∂y. Similarly, ∇⃗ v is defined.)

(b) Show that the function ω must be analytical to be a harmonic function, that is, it must satisfy the Cauchy-Riemann conditions. (Hint: If a function u (x, y) is harmonic, it satisfies the following condition: ∇ ^ 2u = ∂ ^ 2u / ∂x ^ 2 + ∂ ^ 2u / ∂y ^ 2 = 0. In this case, u and v must meet the harmonics condition separately.)