Prove that `tan(ilog_e((a-ib)/(a+ib)))=(2ab)/(a^2-b^2)` (where `a, b in R^+`)

tan (i log ((a-ib)/(a+ib))) = (i) ab (ii) (2ab)/(a^(2) -b^(2)) (iii) (a^( 2) -b^(2))/(ab) (iv) (2ab)/(a^(2)+b^(2))

If (a-ib)/(a+ib)= (1+i)/(1-i) , then show that a+b=0

If a and b are real and i=sqrt(-1) then sin[i ln((a+ib)/(a-ib))] is equal to 1) (2ab)/(a^(2)-b^(2)) 2) (-2ab)/(a^(2)-b^(2)) 3) (2ab)/(a^(2)+b^(2)) 4) (-2ab)/(a^(2)+b^(2))

If (a+ib)(x+iy)=(a^(2)+b^(2))i , then (x,y) is

z=x+iy,z^(1/3)=a-ib,(x)/(a)-(y)/(b)=k(a^(2)-b^(2)) then k is :

If (a+ib)/(c+id)=x+iy, prove that(i) (a-ib)/(c-id)=(x-iy)( ii) (a^(2)+b^(2))/(c^(2)+d^(2))=(x^(2)+y^(2))

Show that if a,b,c,d in R , overline((a+ib)(c+id))=(a-ib)(c-id) .

The value of Arg [i ln ((a-ib)/(a+ib))] , where a and b are real numbers, is

Given that (a_(1)+ib_(1))(a_(2)+ib_(2)) . . . .(a_(n)+ib_(n))=c+id , show that: tan^(-1)((b_(1))/(a_(1)))+tan^(-1)((b_(2))/(a_(2)))+ . . .+tan^(-1)((b_(n))/(a_(n)))=mpi+tan^(-1)((d)/(c)) .

Given that: (a_(1)+ib_(1))(a_(2)+ib_(2)) . . . (a_(n)+ib_(n))=c+id , show that: tan^(-1)((b_(1))/(a_(1)))+tan^(-1)((b_(2))/(a_(2)))+ . . .+tan^(-1)((b_(n))/(a_(n))) =mpi+tan^(-1)((d)/(c)) .