`(i^(365)+i^(246)+i^(95)+i^(35))/(i^(355)+i^(236)+i^(85)+i^(25))-1`

(i^(95)+i^(67)) =

Find the values of following expressions: i^(49)+i^(68)+i^(89)+i^(110) (ii) i^(30)+i^(80)+i^(120) (iii) i^+i^2+i^3+i^4 (iv) i^5+i^(10)+i^(15) (v) (i^(592)+i^(590)+i^(586)+i^(584))/(i^(582)+i^(580)+i^(576)+i^(574)) (vi) 1+i^2+i^4+i^6+i^8+doti^(20) (vii) (1+i)^6+(1-i)^3

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))-1 (ii)(1+i)^6+(1-i)^6

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

Evaluate 2i^(2)+ 6i^(3)+3i^(16) -6i^(19) + 4i^(25)

Evaluate 2i^(2)+ 6i^(3)+3i^(16) -6i^(19) + 4i^(25)

Simplify ( i ^( 238) + i ^( 236) + i ^( 234) + i ^( 232) + i ^( 230))/( i ^( 228) + i ^( 226) + i ^( 224) + i ^( 222) + i ^( 220))

Prove that: (i) (1-i)^(2)=-2i (ii) (1+i)^(4)xx(1+(1)/(i))^(4)=16 (iii) {i^(19)+((1)/(i))^(25)}^(2)=-4 (iv) i^(4n)+i^(4n+1)+i^(4n+2)+i^(4n+3)=0 (v) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25)=1+4i .

Write the following in the form x+iy: (i) (3+2i)(2-i) (ii) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25) . (iii) ((3-2i)(2+3i))/((1+2i)(2-i)) .

Simplify the following : (i) [i^(19) +(1)/(i^(25))]^(2) (ii) [i^(5)- (1)/(i^(3))]^(4)