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If z=x+iy is a complex number with x, ...

If `z=x+iy` is a complex number with `x, y in Q and |z| = 1`, then show that `|z^(2n)-1|` is a rational numberfor every `n in N`.

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  3. If z=x+iy is a complex number with x, y in Q and |z| = 1, then show ...

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

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

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

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

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  8. If fig shows the graph of f(x)=a x^2+b x+c ,t h e n Fig a. c<0 b. b c...

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  9. If det|6i -3i 1 4 3i-1 20 3 i|=x+i y , then a.x=3,y=1 b. x=1...

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

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

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

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

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  14. If the equation 4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0 have a r...

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  15. Express the following in a+i b form: ((cos2theta-isin2theta)^4(cos4...

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  16. The roots of the equation t^3+3a t^2+3b t+c=0a r ez1, z2, z3 which rep...

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  17. Solve the equation (x-1)^3+8=0 in the set C of all complex numbers.

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  18. If 'z, lies on the circle |z-2i|=2sqrt2, then the value of arg((z...

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  19. If the equation whose roots are the squares of the roots of the cubic ...

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  20. If sqrt(3)+i=(a+i b)(c+i d) , then find the value of tan^(-1)(b//a)+ta...

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