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prove that families are orthogonal

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Let the function f(z) = u(x,y) + iv(x,y) be analytic in a domain D, and consider the families of level curves u(x,y) = c1 and v(x,y) = c2. Prove that these families are orthogonal. More precisely, show that if z0 = (x0, y0) is a point in D which is common to u(x,y) = c1 and v(x,y) = c2 and if f'(z0) doesn't equal 0, then the lines tangent to those curves at (x0, y0) are perpendicular.

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