Discussion
True or false: a function whose real and imaginary parts are both harmonic must be analytic.
Answer: D
Harmonicity of each part is necessary but not sufficient: the two must be conjugate, that is linked by the Cauchy-Riemann equations. Taking \( u = x \) with \( v = y \) gives two harmonic functions, yet \( x + iy \) written that way is \( \bar{z} \)'s cousin and fails the equations, so the pairing matters as much as the parts
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