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Prove that the roots of the equation x^4...

Prove that the roots of the equation `x^4-2x^2+4=0` forms a rectangle.

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If alpha,beta are the roots of the quadratic equation a x^2+b x+c=0 , ...

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  2. The locus represented by the equation abs(z-1)=abs(z-i) is

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  3. Prove that the roots of the equation x^4-2x^2+4=0 forms a rectangle.

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  4. If a ,b ,c are non-zero real numbers, then find the minimum value of t...

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  5. If z1a n dz2 are two nonzero complex numbers such that =|z1+z2|=|z1|+|...

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  6. If diagonals of a parallelogram bisect each other, prove that its a rh...

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  7. If a ,b ,c and u ,v ,w are the complex numbers representing the vertic...

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  8. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)++a(n...

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  9. If omega is an imaginary cube root of unity, then (1+omega-omega^2)^7 ...

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  10. If z=x+iy is a complex number with x, y in Q and |z| = 1, then show ...

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  11. Referred to the principal axes as the axes of co ordinates find the eq...

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  12. Find the area bounded by |arg z|lt=pi//4 and |z-1|<|z-3|dot

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  13. Find sum(k=1)^6 (sin,(2pik)/7 -icos, (2pik)/7)=?

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  14. If the equation a x^2+b x+c=0(a &gt;0) has two real roots alphaa n db...

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  15. If fig shows the graph of f(x)=a x^2+b x+c ,t h e n Fig a. c<...

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  16. If |[6i,-3i,1],[ 4, 3i,-1],[ 20, 3,i]|=x+i y , then a.x=3,y=1 b. x=1,y...

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  17. Let z=x+i y be a complex number, where xa n dy are real numbers. Let...

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  18. If z=((sqrt(3))/2+i/2)^5+((sqrt(3))/2-i/2)^5 , then prove that I m(z)=...

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  19. The value of sum(n=1)^(13) (i^n+i^(n+1)), where i =sqrt(-1) equals ...

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  20. If c!=0 and the equation p//(2x)=a//(x+c)+b//(x-c) has two equal roots...

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