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Let z1,z2, z3,......, zn be complex numb...

Let `z_1,z_2, z_3,......, z_n` be complex numbers such that `|z_1|=|z_2|=...=|z_n|=1.` If `z=(sum_(k=1)^n z_k)(sum_(k=1)^n1/(z_k))` then prove that `z` is a real number

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

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  3. Let z1,z2, z3,......, zn be complex numbers such that |z1|=|z2|=...=|z...

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  4. If a ,b , in R such that a+b=1a n d(1-2ab)(a^3+b^3)=12 . The value ...

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  5. If |z|lt=4 , then find the maximum value of |i z+3-4i|dot

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  6. Find the range of f(x)=x^2-x-3.

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  7. If the fraction (x^3 +(a-10)x^2-x+a-6)/(x^3 +(a-6)x^2-x+a-10)reduces t...

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  8. The polynomial f(x)=x^4+a x^3+b x^3+c x+d has real coefficients and f(...

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  9. Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

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  10. If the quadratic equation a x^2+b x+c=0(a >0) has sec^2thetaa n dcos e...

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  11. Find the value of 1+i^2+i^4+i^6++i^(2n)

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  12. Let x ,y ,z in R such that x+y+z=5 and x y+y z+z x=3. Thenwhat is the...

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  13. Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisibl...

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  14. if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+...

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  15. Solve: i x^2-3x-2i=0,

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  16. Let a ,b ,a n dc be distinct nonzero real numbers such that (1-a^3)/a...

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  17. Express each one of the following in the standard form a+i bdot (5+...

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  18. If the cubic 2x^3-9x^2+12 x+k=0 has two equal roots then minimum valu...

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  19. If z=4+isqrt(7) , then find the value of z^2-4z^2-9z+91.

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  20. If the quadratic equation4x^2-2(a+c-1)x+a c-b=0(a > b > c) (a...

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