Q. A complex function 𝑓(𝑧) = 𝑢(𝑥, 𝑦) + 𝑖 𝑣(𝑥, 𝑦) and its complex conjugate 𝑓∗(𝑧) = 𝑢(𝑥, 𝑦) − 𝑖 𝑣(𝑥, 𝑦) are both analytic in the entire complex plane, where 𝑧 = 𝑥 + 𝑖 𝑦 and 𝑖 = √−1 . The function 𝑓 is then given by
Sol:
f(z) = u(x, y) + i v(x, y)
f*(z) = u (x, y) – i v(x, y)
f(z) is analytic function
