If f(z) is a Regular Function, prove that (d²/dx² + d²/dy²)|f(z)|² = 4|f'(z)|² ANALYTIC FUNCTION

[@nxtlev3l371]

wow it was fun, Thanks ♥️

[@suyashsahu6505]

6:47 it should be (du/dy)=-(du/dx)

[@Mdashik77777]

Voice is so beautiful 😍

[@JaswinderKaur-kk5kl]

Thank you! God Bless!

[@bosssstorage3201]

💯 agree

[@mubx4323]

where is this question from?

[@JaswinderKaur-kk5kl]

Yes , the Book is ' Functions of Complex Variables' by J.N.Sharma

[@charukesisivaraj5575]

Nothing can understable....can you please explain your steps clearly....

[@JaswinderKaur-kk5kl]

Every step is clearly explained. Sorry, if it is not easy to understood. Yes, the steps are: 1) f(z) = u+iv 2) |f(z)|² is in terms of u and v which are dependent on both x and y variables so I have taken this as a function of x and y as phi(x,y). 3) Finding 🔸️ d(phi)/dx 🔸️d(phi)/dy 🔸️d²(phi)/dx² = d/dx of d(phi)/dx 🔸️d²(phi)/dy² = d/dy of d(phi)/dy [ Or simply replacing x with y for last one using d²(phi)/dx² to get d²(phi)/dy²] 4) Adding d²(phi)/dx² & d²(phi)/dy² and then using Cauchy Riemann Equations ( mentioned in green colored in steps) and Laplace's equations to get the required result. 4) Replacing back phi(x,y) with |f(z)|² and at last using the Result on the right hand side that, | any complex no.|² = (real part)² + (imaginary part)² I hope it is now clear to you. If not , kindly mention the step which is still not cleared. Thank you!

[@TechnicalSoumyak]

Practice hoga tabhi to samjhega na.mam clearly explained