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Show that e^(2m itheta)((icottheta+1)/(i...

Show that `e^(2m itheta)((icottheta+1)/(i cottheta-1))^m=1.`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find real value of x and y for which the complex numbers -3+i x^2y ...

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  2. Show that ((x+b)(x+c))/((b-a)(c-a))+((x+c)(x+a))/((c-b)(a-b))+((x+a)(x...

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  3. Show that e^(2m itheta)((icottheta+1)/(i cottheta-1))^m=1.

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  4. A certain polynomial P(x)x in R when divided by kx-a ,x-ba n dx-c lea...

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  5. It is given that complex numbers z1 and z2 satisfy |z1|=2 and |z2|=3....

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  6. If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b...

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  7. If z1^2+z2^2+2z1.z2.costheta= 0 prove that the points represented by ...

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  8. If (a^2-1)x^2+(a-1)x+a^2-4a+3=0 is identity in x , then find the val...

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  9. Show that a real value of x will satisfy the equation (1-i x)//(1+i x)...

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  10. Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=...

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  11. If a+i b=((x+i)^2)/(2x^2+1), prove that a^2+b^2=((x^2+1)^2)/((2x^2+1)^...

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  12. If the roots of the equation x^2-8x+a^2-6a=0 are real distinct, then f...

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  13. Solve :z^2+|z|=0 .

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  14. If roots of equation x^2-2c x+a b=0 are real and unequal, then prove ...

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  15. Find the range of real number alpha for which the equation z+alpha|z-1...

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  16. If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, sho...

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  17. If (1+i)^2 /(3 - i)=Z , then Re(z) =

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  18. Find the quadratic equation with rational coefficients whose one root ...

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  19. Let z be a complex number satisfying the equation (z^3+3)^2=-16 , then...

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  20. If P(x) = ax^2+bx+c, and Q(x) = -ax^2+dx+c, acne 0, then prove that P(...

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