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An entire function f such that f(x+iy) = u(x)+iv(y) must be of the form f(z)= Az+B with A is a real number and B is a complex number.Is it true?

If f is a complex valued continuous function on C,then I = Integral (f(z)-f(1/z))/z =0 where path if integration is unit circle.Is this statement true?

Sketch the families of curves of component functions u and been f(z)= z-1/z+1

Integral dz/(z^2 - 1)^2 +3

If a Mobius transformation T carries z1 and z2 in to same number w1, then either z1=z2 or else T is a constant map. Is this statement true or false? why?

Show that integral dz/(z^2-1)^2+3=π/2√2, where path of integration is unit circle in the positive sense

Find the image of the half plane y>1 under the transformation w=(1-i)z

Is there any analytic function fexist in a neighborhood of 0 whose square is z?

If a Möbius transformation T carries z1 and z2 into a same number w1,then either z1=z2 or else T is a constant map

If a Möbius transformation T carries z1 and z2 into a same number w1,then either z1=z2 or else T is a constant map.Is this statement true or false ?why?

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