i) If `a = \frac{1+i}{\sqrt{2}}` then show that `1+a^2+a^4+a^6=0`
ii) If `x = 2-i\sqrt{3}` then find the value of `2x^4 - 5x^3 - 3x^2 + 41x - 35`
iii) If `x = 2 + 3i` then find the value of `x^3 - 4x^2 + 13x + 5`
iv) If `x = -1 + i\sqrt{2}` then find the value of `x^4 + 4x^3 + 6x^2 + 4x + 9`