If `(x+i y)^3=u+i v ,`then show that `u/x+v/y=4(x^2-y^2)`. – InterviewSolution

InterviewSolution

1.	If `(x+i y)^3=u+i v ,`then show that `u/x+v/y=4(x^2-y^2)`.
Answer» `(u+iv)=(x+iy)^(3)=x^(3)-iy^(3)+3ixy(x+iy)` `rArr" "(u+iv)=(x^(3)-3xy^(2))+i(3x^(2)y-y^(3))` `rArr" "u=x^(3)-3xy^(2))+3x^(2)y-y^(3)` `rArr" "((u)/(x)+(v)/(y))=(x^(2)-3y^(2))+(3x^(2)-y^(2))=4(x^(2)-y^(2))`.

Discussion

No Comment Found

Related InterviewSolutions

Convert the following in the polar form : (i) `(1+7i)/((2-i)^2)`(ii) `(1+3i)/(1-2i)`
Solve: `x^(2) + 3ix + 10 = 0`
Express `(2 + 3i)^(3)` in the form `(a + ib).`
Express `(2-3i)^(3)` in the form (a + ib).
Solve the system of equations `R e(z^2)=0, |z|=2`
Solve the equation, `z^(2) = bar(z)`, where z is a complex number.
Convert each of the following complex numbers into polar form: `{:((i),3,(ii),-5,(iii),i,(iv),-2i):}`
If the complex number `Z_(1)` and `Z_(2), arg (Z_(1))- arg(Z_(2)) =0`. then show that `|z_(1)-z_(2)| = |z_(1)|-|z_(2)|`.
`Z_1 and Z_2` are two complex numbers represented by the plans A and B in the argand Plane `Z_! And Z_2` are the roots of `Z^2+pZ+q = 0`. `/_AOB = alpha` `alpha!= 0` and O is origin and OA = OB, then `p^2/q` is equal to
For all complex numbers `z_(1) and z_(2)`, prove that `|z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2(|z_(1)|^(2)+|z_(2)|^(2))`.