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Show that: sum(r=0)^(n-1)|z1+alpha^r z2|...

Show that: `sum_(r=0)^(n-1)|z_1+alpha^r z_2|^2=n(|z_1|^2+|z_2|^2),w h e r e, alpha ; r=0,1,2,...,(n-1)` , are the nth roots of unity and `z_1, z_2` are any two complex numbers.

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. Solve sqrt(5x^2-6x+8)-sqrt(5x^2-6x-7)=1.

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  3. Show that: sum(r=0)^(n-1)|z1+alpha^r z2|^2=n(|z1|^2+|z2|^2),w h e r e,...

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  4. Solve sqrt(x^2+4x-21)+sqrt(x^2-x-6)=sqrt(6x^2-5x-39.)

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  5. If alpha=(z-i)(z+i), show that, when z lies above the real axis, alpha...

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  6. Solve 4^x+6^x=9^xdot

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  7. Let x1, x2 are the roots of the quadratic equation x^2+a x+b=0,w h e r...

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  8. Solve 3^(2x^2-7x+7)=9.

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  9. Plot the region represented by pi/3lt=a r g((z+1)/(z-1))lt=(2pi)/3 in ...

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  10. How many solutions does the equation(8^x + 27^x)/(12^x +18^x) = 7/6hav...

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  11. Is the following computation correct? If not give the correct compu...

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  12. Consider an equilateral triangle having verticals at point A(2/sqrt3 e...

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  13. Find the number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=...

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  14. Find the value of (i) (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(58...

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  15. Let z,z(0) be two complex numbers. It is given that abs(z)=1 and the n...

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  16. Show that the equation a z^3+b z^2+ barb z+ bara =0 has a root alpha ...

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  17. If nge3and1,alpha(1),alpha(2),alpha(3),...,alpha(n-1) are the n,nth ...

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  18. How many roots of the equation 3x^4+6x^3+x^2+6x+3=0 are real ?

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  19. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Arg and plane, the...

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  20. Find the value of k if x^3-3x+k=0 has three real distinct roots.

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