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Fill in the blanksIf`x<0,y<0,x+y+(x//y)=(1//2)a n d (x+y)(x//y)=-(1//2),t h e nx=___a n dy=___dot`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the equations x^2+ax+b=0 and x^2+bx+a=0 have one common root. Then ...

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  2. Find all possible values of sqrt(i)+sqrt(-i)dot.

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  3. Fill in the blanksIfx<0,y<0,x+y+(x//y)=(1//2)a n d (x+y)(x//y)=-(1//2...

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  4. Find the square roots of the following: (i) 7-24 i

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  5. True or false The equation2x^2+3x+1=0 has an irrational root.

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  6. If z!=0 is a complex number, then prove that R e(z)=0 rArr Im(z^2)=0.

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  7. If l ,m ,n are real and l!=m , then the roots of the equation (l-m)x...

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  8. Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0\ ,...

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  9. If x ,y and z are real and different and u=x^2+4y^2+9z^2-6y z-3z x-2x ...

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  10. If (x+i y)^3=u+i v , then show that u/x+v/y=4(x^2-y^2)

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  11. Let a >0,b >0 and c >0 . Then, both the roots of the equation a x^2+b ...

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  12. If the sum of square of roots of the equation x^2+(p+i q)x+3i=0 is 8, ...

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  13. Column I ...............................................................

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  14. If sqrt(x+i y)=+-(a+i b), then findsqrt( -x-i ydot)

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  15. Match the following for the equation x^2+a|x|+1=0,w h e r ea is a para...

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  16. Find the ordered pair (x ,y) for which x^2-y^2-i(2x+y)=2idot

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  17. If a ,b ,c are non zero complex numbers of equal modlus and satisfy a ...

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  18. Let z be not a real number such that (1+z+z^2)//(1-z+z^2) in R , then...

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  19. Let a is a real number satisfying a^3+1/(a^3)=18 . Then the value of a...

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  20. Find non zero integral solutions of |1-i|^x=2^xdot

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