निम्नलिखित के मान कीजिए-
(i) `i^(7)+i^(17)+i^(12)` (ii) `i^(11)+i^(-11)`
(iii) `i^(3)+1/i^(3)` (iv) `1+i^(2)+i^(6)+i^(8)`

Find the values of the following : (i) i^(7)+i^(17)+i^(12) (ii) i^(11)+i^(-11) (iii) i^(3)+(1)/(i^(3)) (iv) 1+i^(2)+i^(6)+i^(8)

Find the values of the following : (i) i^(7)+i^(17)+i^(12) (ii) i^(11)+i^(-11) (iii) i^(3)+(1)/(i^(3)) (iv) 1+i^(2)+i^(6)+i^(8)

Simplify the following : (i) i^(97) (ii) i^(8) (iii) (1)/(i^(3)) (iv) (-i)^(14) (v) i^(-22) (vi) i^(-63)

Simplify the following : (i) i^(97) (ii) i^(8) (iii) (1)/(i^(3)) (iv) (-i)^(14) (v) i^(-22) (vi) i^(-63)

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) .

Evaluate the following : (i) i^(7) (ii) i^(51) (iii) (1)/(i) (iv) i^(-71) (v) (i^(37)+(1)/(i^(67)))

Evaluate the following (i) i^(9) (ii) i^(342) (iii) i^(998) (iv) i^(-63) (v) (i^(3)+(1)/(i^(3)))

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)

. (i) i= 2 A (ii) i_1 = (10)/(3) A (iii) i_2 = - (4)/(3) A .

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