Determine the constants a and b if the function f(z) is analytic

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Question: Determine the constants a and b in order that the function
f(z) = (x2 + ay2 - 2xy) + i(bx2 - y2 + 2xy) should be analytic. Hence find f1(z).

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Evaluated where f(2)=y-x-3xi from=0 to z = 1+i along

the path

i) from (0, 0) to A(1, 0) and to B(1, 1)

ii) y = x.

cookingwithutkarsh
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Does anyone know from which book this question has been taken?

devangsaini
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Ma'am how we can consider
ay+y= -bx+x
Is true when ay+y=0 and -bx+x=0

I mean ma'am can you explain this step (ay+y=0 and -bx+x=0) please.

ratnadeepdas