и (х, у) 3D х3 +х — 3ху? What is the imaginary part of the analytic complex function if(z) = u(x, y) + i v(x, y) whose real part is given above?

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A: We have to multiply the given three complex numbers.

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A: Here we use CRE equation to prove this

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A: Given function : f(z) = ei z2

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Q: (a) S,(Iz – il2 – z) dz along the semicircle y = 1+ et“, 0 < t < n; -

A: ∫γz-i2-zdz=∫0π1+eit-i2-1-eitieitdt=∫0π1+cost2+sint-12-1-eitieitdt=∫0π1+cos2t+2cost+sin2t+1-2sint-1-e…

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Q: fy your answers. f(z) = zRez; (b) f(z) = Z;

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