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Prove that the equation Z^3+i Z-1=0 has ...

Prove that the equation `Z^3+i Z-1=0` has no real roots.

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. P(z) be a variable point in the Argand plane such that |z|=minimum {|z...

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  2. If the equation a x^2+b x+c=0,a ,b ,c , in R have none-real roots, t...

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  3. Prove that the equation Z^3+i Z-1=0 has no real roots.

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  4. The locus of point z satisfying Re(1/z)=k, where k is a non-zero real ...

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  5. If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p...

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  6. Find the square root 9+40 idot

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  7. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic e...

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  8. Let a be a complex number such that |a|<1a n dz1, z2,z3,... be the ve...

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  9. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

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  10. If the ratio of the roots of the equation x^2+p x+q=0 are equal to rat...

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  11. Let z=1-t+isqrt(t^2+t+2), where t is real parameter. The locus of z in...

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  12. If sintheta,costheta be the roots of a x^2+b x+c=0 , then prove that b...

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  13. Express the following complex numbers in a+i b form: ((3-2i)(2+3i))/((...

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  14. If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely i...

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  15. z^2+zabsz+absz^2=0 then the locus of z is

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  16. If the sum of the roots of the equation 1/(x+a)+1/(x+b)=1//c is zero,...

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  17. Solve the equation x^2+p x+45=0. it is given that the squared differen...

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  18. Find the least positive integer n such that ((2i)/(1+i))^n is a positi...

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  19. z1a n dz2 lie on a circle with center at the origin. The point of inte...

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  20. If alpha,beta are the roots of the equation 2x^2-35x+2=0 , the find ...

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