Home
Class 11
MATHS
If (x+iy)^(1//3) = a+ib, where a, b, x, ...

If `(x+iy)^(1//3) = a+ib`, where `a, b, x, y in R` show that `x/a - y/b = -2(a^(2) + b^(2))`.

A

`a^2-b^2`

B

`4(a^2-b^2)`

C

`4(a^2+b^2)`

D

`a^2+b^2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

If (x+iy)^(3) = u + iy , then show that u/x + v/y = 4(x^(2)-y^(2))

If (x+iy)^(3)=u+iv ,then show that u/x+v/y =4(x^(2) -y^(2)) ?

If (x+iy)^(1//3)=a+ib,"where "i=sqrt(-1),then ((x)/(a)+(y)/(b)) is equal to

If x + iy = sqrt((a + ib)/(c + id)) Prove that x^(2) + y^(2) = sqrt(( a^(2) + b^(2))/(c^(2) + d^(2)))

Area of the triangle with vertices (a, b) (x_(1), y_(1)) and (x_(2), y_(2)) , where a, x_(1), x_(2) are in GP. with common ratio r and b, y_(1), y_(2) are in GP. with common ratio s is :

Area of the triangle with vertices (a, b ), (x_(1), y_(1)) and (x_(2), y_(2)) , where a, x_(1), x_(2) are in G.P. with common ratio r and b, y_(1), y_(2) are in G.P. with common ratio s is :

If x =1 + a + a^(2)+"………" to oo and y = 1+ b + b^(2) +"………" to oo where a and b are proper fraction, then 1 + ab + a^(2) b^(2) + "……." to oo equals :

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

If x+iy = (a+ib)/(a-ib) , prove that x^(2) + y^(2)=1 .

(ii) If x + iy =(a+ib)/(a-ib) prove that x^(2) + y^(2)=1