The function $$$w = u + iv = {1 \over 2}\log \left( {{x^2} + {y^2}} \right) + i{\tan ^{ - 1}}\left( {{y \over x}} \right)$$$ is not analytic at the point.

For solving algebraic and transcendental equation which one of the following is used?

Newton $$-$$ Raphson formula to find the roots of an equation $$f(x)=0$$ is given by

The real root of the equation $$x{e^x} = 2$$ is evaluated using Newton $$-$$ Raphson's method. If the first approximation of the value of $$x$$ is $$0.8679,$$ the $${2^{nd}}$$ approximation of the value of $$x$$ correct to three decimal places is