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Let z be a complex number such that the ...

Let `z` be a complex number such that the imaginary part of `z` is nonzero and `a = z^2 + z + 1` is real. Then a cannot take the value

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the difference between the roots of the equation x^2+""a x""+""1...

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  2. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

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  3. Let z be a complex number such that the imaginary part of z is nonzero...

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  4. For the equation 3x^2+p x+3=0,p >0, if one of the root is square of th...

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  5. Let z,w be complex numbers such that barz+ibarw=0 and arg zw=pi Then a...

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  6. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) be the minimum value of f(x)do...

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  7. For any two complex numbers z1 and z2, , prove that Re (z1 z2) = Re ...

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  8. If alphaa n dbeta are the roots of the equation x^2+b x+c=0,where <mat...

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  9. If omega(!= 1) be an imaginary cube root of unity and (1+omega^2)^n=(...

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  10. If b &gt; a , then the equation (x-a)(x-b)-1=0 has (a) both roots i...

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  11. Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...

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  12. The equation sqrt(x+1)-sqrt(x-1)=sqrt(4x-1) has a. no solution b. o...

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  13. If z1, z2 are complex number such that (2z1)/(3z2) is purely imaginary...

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  14. If the roots of the equation x^2-2a x+a^2-a-3=0 are real and less than...

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  15. If z(1+a)=b+i ca n da^2+b^2+c^2=1, then [(1+i z)//(1-i z)= A. (a+i b...

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  16. A value of b for which the equation x^2+b x-1=0,x^2+x+b=0 have one roo...

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  17. If z1, z2, z3 are three complex, numbers and A=[[a r g z1,a r g z3,a...

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  18. Let p and q be real numbers such that p!=0,p^3!=q ,and p^3!=-qdot If a...

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  19. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0, then the...

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  20. Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,...

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