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Find real value of theta for which (3+2i...

Find real value of `theta` for which `(3+2i sin theta)/(1-2i sin theta)` is purely real.

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

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  2. If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta...

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  3. Find real value of theta for which (3+2i sin theta)/(1-2i sin theta) i...

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

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

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

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

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

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

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

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

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

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

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  15. Find real value of xa n dy for which the complex numbers -3+i x^2ya n...

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

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  18. A certain polynomial P(x), x in R when divided by x-a ,x-b and x-c le...

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

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

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