Home
Class 11
MATHS
tan(ilog((a-ib)/(a+ib)))= (i) ab (ii)...

`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)`

Text Solution

Verified by Experts

`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`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

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))

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

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

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

(a^2+b^2+2ab)-(a^2+b^2-2ab)

tan [ i log ((a - ib)/(a + ib )) ] is equal to : a) ab b) (2 ab)/( a ^(2) - b ^(2)) c) (a ^(2) - b ^(2))/( 2 ab) d) (2 ab)/( a ^(2) + b ^(2))

Prove that tan(i log_(e)((a-ib)/(a+ib)))=(2ab)/(a^(2)-b^(2)) (where a,b in R^(+))

If cos theta = (a cos phi + b) / (a + b cos phi) then (tan ((theta) / (2))) / (tan ((phi) / (2))) = (A) ( ab) / (a + b) (B) (a + b) / (ab) (C) sqrt ((a + b) / (ab)) (D) sqrt ((ab) / (a + b))