[" (g) "(i^(4n+1)-i^(4n-1))/(2)],[" संकेत : "i^(4n)=1]

Evaluate (i^(4n+1) - i^(4n-1)) .

1 + i^(2n) + i^(4n) + i^(6n)

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 .

If n is any positive integer,write the value of (i^(4n+1)-i^(4n-1))/(2)

Prove that (1 + i)^(n) + (1 - i)^(n) = 2^((n + 2)/(2)) cos (n pi)/(4)

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)

If n is any positive integer then the value of (i^(4 n+1)-i^(4 m-1))/(2)=

If n is any positive integer, write the value of (i^(4n+1)-i^(4n-1))/2 .