If f(x, y) = x 3 – 3xy 2 of an...

v is its harmonic conjugate and v(x, y) = 3x 2 y – y 4 + c, c is real constant

–v is its harmonic conjugate and v(x, y) = y 2 – 3x 2 y + c, c is real constant

v is its harmonic conjugate and v(x, y) = 3x 2 y – y 4 + c, c is any constant

–v is its harmonic conjugate and v(x, y) = y 3 – 3x 2 y + c, c is any constant

If f(x, y) = x³– 3xy² of an analytic function f(z) = u + iv, then

v is its harmonic conjugate and v(x, y) = 3x²y – y⁴+ c, c is real constant

–v is its harmonic conjugate and v(x, y) = y²– 3x²y + c, c is real constant

v is its harmonic conjugate and v(x, y) = 3x²y – y⁴+ c, c is any constant

–v is its harmonic conjugate and v(x, y) = y³– 3x²y + c, c is any constant