For real numbers we only had x = -ln(φ)/ln(0.8) as a solution. But with complex numbers there can be multiple solutions since the complex log is multivalued. Since there were two possibilities for p which are valid with the complex log, all solutions from any branch are in the form z = (-ln(φ) + 2kπi)/ln(0.8) or z = (ln(φ) + (2k+1)πi)/ln(0.8) for any integer k.