" (ti) "(1+i^(3))(1+(1)/(i))^(2)(r^(4)+(1)/(r^(4)))

Simplify : (1+i^(3))(1+(1)/(i))^(2)(i^(4)+(1)/(i^(4)))

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 .

((1)/(r)+(1)/(r_(1))+(1)/(r_(2))+(1)/(r_(3)))^(2)=(4)/(r)((1)/(r_(1))+(1)/(r_(2))+(1)/(r_(3)))

Prove that ((1)/(r)-(1)/(r_(1)))((1)/(r)-(1)/(r_(2)))((1)/(r)-(1)/(r_(3)))=(abc)/(Delta^(3))=(4R)/(r^(2)s^(2))

Find the sum to n terms of the series (1)/(1+1^(2)+1^(4))+(2)/(1+2^(2)+2^(4))+(3)/(1+3^(2)+3^(4))+ that means t_(r)=(r)/(r^(4)+r^(2)+1) find sum_(1)^(n)

((1+i)/(1-i))^(4)+((1-i)/(1+i))^(4)=(A)1(B)2(C)3(D)4

Show that (r_(1)+ r _(2))(r _(2)+ r _(3)) (r_(3)+r_(1))=4Rs^(2)

Show that (r_(1)+ r _(2))(r _(2)+ r _(3)) (r_(3)+r_(1))=4Rs^(2)

Prove that sum_(r=0)^(n)C_(r)(-1)^(r)[i+i^(2r)+i^(3r)+i^(4r)]=2^(n)+2^((n)/(2)+1)cos(n pi/4), where i=sqrt(-1) -