(1)/(i)-(1)/(i^(2))+(1)/(i^(3))-(1)/(i^(4))

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

(Acitity) Express (1)/(i^(1)) + (2)/( i ^(2)) +(3)/( i ^(3)) + (5)/( i ^(4)) in the form of (a + ib).

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

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

The conjugate of a complex number is 1/(i-1) . Then the complex number is (1) (-1)/(i-1) (2) 1/(i+1) (3) (-1)/(i+1) (4) 1/(i-1)

(1)/(1-2i)+(3)/(1+4i)

1+(1+i)+(1+i)^(2)+(1+i)^(3)=

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 .

Reduce ((1)/(1-4i)-(2)/(1+i))((3-4i)/(5+i)) to the standard form.