2.i^(1948)-i^(-1869)

Simplify the following: i^(1948) + i^(-1869

Simplify the following : (i) i^7 " " (ii) i^(1729) " " (iii) i^(-1924) + i^(2018) " " (iv) sum_(n=1)^(102) i^(n) " " (v) i i^2 i^3 …..i^(40)

The value of (i^(592)+i^(590)+i^(586)+i^(584))/(i^(582)+i^(580)+i^(578)+i^(576)+i^(574)) will be

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

Evaluate ((i^(180)+i^(178)+i^(176)+i^(174)+i^(172))/(i^(170)+i^(168)+i^(166)+i^(164)+i^(162))) .

Write the following in the form x+iy: (i) i+i^(2)+i^(3)+i^(4) (ii) i^(4)+i^(8)+i^(12)+i^(16) (iii) i+i^(5)+i^(9)+i^(13) (iv) i^(9)+i^(10)+i^(11)+i^(12) .

Let i^(2)=-1 , then (i^(10)-1/(i^(11)))+(i^(11)-1/(i^(12)))+(i^(12)-1/(i^(13)))+(i^(13)-1/(i^(14)))+(i^(14)+1/(i^(15))) is equal to a) -1+i b) -1-i c) 1+i d) -i

If (i^(4)+i^(9)+i^(26))/(2-i^(8)+i^(10)-i^(15))=A+i B then (A, B)=

Find the value of (i) (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+i^(580)+i^(578)+i^(576)+i^(574)) (i) -1 (ii) (1+i)^6+(1-i)^6