`1+i^(10)+i^(110)+i^(1000)`

Prove that: (i) 1+i^(10)+i^(100)-i^(1000)=0 (ii) i^(107)+i^(112)+i^(117)+i^(122)=0 (iii) (1+i^(14)+i^(18)+i^(22)) is real number.

Prove that: (i) 1+i^(2)+i^(4)+i^(6)=0 (ii) 1+i^(10)+i^(100)+i^(1000)=2 (iii) i^(104)+i^(109)+i^(114)+i^(119)=0 (iv) 6i^(54)+5i^(37)-2i^(11)+6i^(68)=7i (v) (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+i^(580)+i^(578)+i^(576)+i^(574))=-1

Show that Find the value of: 1+ i^10 + i^100 - i^1000 = 0

Show that 1+i^(10)+i^(20)+i^(30) is a real number.

Show that 1+i^(10)+i^(20)+i^(30) is a real number.

Simplify the following : (i) 1+ i^(5)+i^(10)+i^(15) (ii) (1+i)^(4)+(1+(1)/(i))^(4) (iii) i^(n)+i^(n+1)+i^(n+2)+i^(n+3)

Simplify the following : (i) 1+ i^(5)+i^(10)+i^(15) (ii) (1+i)^(4)+(1+(1)/(i))^(4) (iii) i^(n)+i^(n+1)+i^(n+2)+i^(n+3)

Prove that : 1+ i^10+i^100-i^1000=0 .