हल करे:
`(1-i)^(-2)+(1+i)^(-2)`

((1-i)^(3))/(1-i^(3))=-2

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

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

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 ((1+i)/(1-i))^(2) - ((1-i)/(1+i))^(2) = x + iy then find (x,y).

((1+i)/(1-i))^(2) + ((1-i)/(1+i))^(2) is equal to :

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

((1-i)/(1+i))^2=