On infinite area for complex exponential function

This paper shows via a reduced family of examples, the relaxed Newtonʹs method is applied to complex exponential function F(z)=zez and F(z)=zez2, the basin of roots has infinite area. In addition, we examined their computer pictures which are fractals for the relaxed Newtonʹs basin. In fact, computer experiments F(z)=P(z)ez and F(z)=P(z)ez2, indicate this to hold for arbitrary non-constant polynomial P(z).