Complex analysis show that f(z) is holomorphic

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In this video explained example is a complex analysis holomorphic. This is easy method and use in Cauchy Riemann equations.
Quantum mechanics: In quantum mechanics the wave function of a particle can be represented by a complex function that satisfies the Schrödinger equation. This function can be decomposed into a pair of conjugate harmonic functions which can be used to compute the probability distribution of the particle's position and momentum.

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