Question

if a=1+i/√2 then find the value of a6+a4+a2+1.

Answer 1

a^6+a^4+a^2+1=a^4(a^2+1)+1 (a^2+1)
= (a^2+1)(a^4+1).... (eq 1)
here,
a=(1+i)/root 2
or root2*a=1+i
squatting both sides
2a^2=(1+i)^2
or 2a^2=1+2i+i^2
or 2a^2=1+2i+(-1) since i^2=(-1)
a^2=i
or a^4=i^2=(-1)
so from eq (1) ....

a^6+a^4+a^2+1 =(a^2+1)(a^4+1)= (i+1)(-1+1)= 0*(i+1)=0