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Prove that tan(iloge((a-ib)/(a+ib)))=(2...

Prove that `tan(ilog_e((a-ib)/(a+ib)))=(2ab)/(a^2-b^2)` (where `a, b in R^+`)

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find real theta such that (3+2isintheta)/(1-2isintheta) is purely real...

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  2. If the roots of the equation a x^2+b x+c=0 are of the form (k+1)/k and...

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  3. Prove that tan(iloge((a-ib)/(a+ib)))=(2ab)/(a^2-b^2) (where a, b in ...

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  4. If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are t...

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  5. Find the real part of (1-i)^(-i)dot

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  6. The equation (x^2+x+1)^2+1=(x^2+x+1)(x^2-x-5) for x in (-2,3) will h...

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  7. Convert of the complex number in the polar form: 1-i

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  8. If alpha,beta are the roots of a x^2+c=b x , then the equation (a+c y)...

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  9. If z=r e^(itheta) , then prove that |e^(i z)|=e^(-r sintheta)

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  10. If the roots of the equation x^2+2a x+b=0 are real and distinct and th...

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  11. Z1!=Z2 are two points in an Argand plane. If a|Z1|=b|Z2|, then prove t...

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  12. If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratio of r...

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  13. Find real value of x and y for which the complex numbers -3+i x^2y ...

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

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

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

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

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

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  20. 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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