If f(z)=u+iv is an Analytic function such that f'(z)≠0, Prove that : {(∂²/∂x²)+(∂²/∂y²)}log|f'(z)|=0

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#25 || Problem# ||If f(z) is analytic, show that [𝝏^𝟐/〖𝝏𝒙〗^𝟐 +𝝏^𝟐/〖𝝏𝒚〗^𝟐 ] |𝒇(𝒛)|^𝟐=𝟒|𝒇^′ (𝒛)|^𝟐 ||

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#26 || Problem#6 || show that [𝝏/𝝏𝒙 |𝒇(𝒛)|]^𝟐+[𝝏/𝝏𝒚 |𝒇(𝒛)|]^𝟐=|𝒇^′ (𝒛)|^𝟐 || 18MAT41||

If f(z)=u+iv is analytic and uv = a constant then f(z) is a constant proof by Jini Varghese