i^(37)+(1)/(i^(67))

Express each of the following complex number in the form a+ib: i^(37)xx(1)/(i^(67))

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

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

The value of (i^(5)+i^(6)+i^(7)+i^(8)+i^(9))/(1+i) is (1)/(2)(1+i)(b)(1)/(2)(1-i)(c)1(d)(1)/(2)

If ((1+i)/(1-i))^(3)-((1-i)/(1+i))^(3)=x+i y then (x, y)=

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

Evaluate : (i) i^(23)" "(ii) i^(998)" "(iii)i^(-998)" "(iv) i^(-71) (v) (sqrt(-1))^(91)" "(vi) (i^(37)xx i^(-61))" "(vii) i^(-1)

Evaluate : (i) (2^(38) + 2^(37) + 2^(36))/(2^(39) + 2^(38) + 2^(37)) (ii) [(64^((1)/(2)))^((1)/(6))]^(2)

((1+i)/(1-i))^(4)+((1-i)/(1+i))^(4)=

((1+i)/(1-i))^4+((1-i)/(1+i))^4=