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If (x+iy)^(3)= u +iv, then show that (u)...

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

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NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. If (x+iy)^(3)= u +iv, then show that (u)/(x)+(v)/(y)=4(x^(2)-y^(2)).

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  2. If p,q are the roots of ax^(2)-25x+c=0, then p^(3)q^(3)+p^(2)q^(3)+p^(...

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  3. If the ratio of roots of x^(2)+bx+c=0" and "x^(2)+qx+r=0 is the same, ...

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  4. Area of the triangle in the Argand diagram formed by the complex numbe...

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  5. If omega is an imaginary cube root of 1, then (1+omega-omega^(2))^(5)+...

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  6. If |z-3+i|=4, then the locus of z is

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  7. If x satisfies x^(2)-2x cos theta +1=0, then the value of x^(n)+((1)/(...

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  8. The value of [((-1+isqrt(3)))/(2)]^(3n)+[((-1-isqrt(3)))/(2)]^(3n) is

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  9. If theta= (pi)/(6), then the 10th term of the series 1+(cos theta +isi...

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  10. If 4=5i is a root of the quadratic equation x^(2)+ax+b=0, then (a,b)=

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  11. If alpha" and "beta are the roots of the quadratic equation 4x^(2)+3x+...

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  12. If alpha" and "beta are the roots of ax^(2)+bx+c=0 and alpha+k, beta+k...

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  13. If 3p^(2)=5p+2" and "3q^(2)= 5q+2, where p ne q, then the equation wh...

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  14. The value of ((-1+sqrt(-3))/(2))^(26)+((-1-sqrt(-3))/(2))^(26) is

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  15. If (sqrt(3)-i)^(50)= 2^(48)(x-iy), then x^(2)+y^(2) is equal to

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  16. The value of (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+i^(580...

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  17. If |(z-i)/(z+i)|=1, then the locus of z is

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  18. The condition that one root of the equation ax^(2)+bx+c=0 may be squar...

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  19. If alpha is one root of the equation 4x^(2)+2x-1=0, then the other roo...

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  20. If the roots of the equation (a)/(x-a)+(b)/(x-b)=1 are equal in magnit...

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  21. The equation of smallest degree with real coefficients having 2+i3 as ...

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