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If f(z)= |z1²., at what points are the Cauchy-Riemann equations satisfied? Justify.

If f(z)= |z1²., at what points are the Cauchy-Riemann equations satisfied? Justify.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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SOLVE STEP BY STEP IN DIGITAL FORMAT ÿ » Ü ¸ 3 * * * @ ! ! ?? !! ? ?! ¿¡ !?! W X i X X X X X X ♫♬b # DOOO * If f(z)= |z|2., at what points are the Cauchy-Riemann equations satisfied? Justify. * ++ * † ☨ + +9 +X+OP東方+中 (*<RO O °C °F ****** AVADA VAA ▷ *** VO
Transcribed Image Text:SOLVE STEP BY STEP IN DIGITAL FORMAT ÿ » Ü ¸ 3 * * * @ ! ! ?? !! ? ?! ¿¡ !?! W X i X X X X X X ♫♬b # DOOO * If f(z)= |z|2., at what points are the Cauchy-Riemann equations satisfied? Justify. * ++ * † ☨ + +9 +X+OP東方+中 (*<RO O °C °F ****** AVADA VAA ▷ *** VO
Expert Solution
Step 1

Let z=x+iy and f(z)=u(x,y)+iv(x,y) .

Then f is said to satisfy the Cauchy-Riemann equations at a point z0=(x0 , y0) , if 

                         ux(x0,y0)=vy(x0,y0)  and  uy(x0,y0)=-vx(x0,y0) ; where ux=∂u∂x, uy=∂u∂y and so on.

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