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If φ(x, y) and ψ (x, y) are functions with continuous second derivatives, then φ(x, y) + iψ(x, y)
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δφ = - δψ , δφ = δψ δx δx δy δy -
δφ = - δψ , δφ = δψ δy δx δx δy -
δ²φ = - δ²ψ , δ²φ = δ²ψ = 1 δx² δy² δx² δy² -
δφ = - δφ , δ²φ = δ²ψ = 0 δx² δy² δx² δy²
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Correct Option: B
Can be expressed as an analytic function of
φ + iψ(i = √-1) , when The necessary condition for a function
f (z) = φ(x,y) + i ψ (x, y) to be analytic
| (i) | = | δx | δy |
| (ii) | = | δy | δx |
are known as Cauchy Rieman equations, provided
| , | , | | , | exists. | | δx | δy | δx | δy |
