1.

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

Answer» `a + ib = r e^(i theta)`
`r = sqrt(a^2 + b^2)`
`theta = tan^-1(b/a)`
`a - ib = r e^(- i theta) `
`i log ( (a-ib)/(a + ib)) = i log( (r e^(_i theta))/(r e^(i theta))) `
`= i log_e e^(-2 i theta) `
`= i(-2 i theta) `
`= 2 theta`
`2 tan^-1(b/a) `
`= tan^-1((2b/a)/(1- b^2/a^2)) = tan^-1((2ab)/(a^2- b^2))`
`tan( tan^-1((2ab)/(a^2 - b^2))) = (2ab)/(a^2 - b^2)`
option 2 is correct


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