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Fill in the blanks If 2+isqrt(3) is a ro...

Fill in the blanks If `2+isqrt(3)` is a root of the equation `x^2+p x+q=0,w h e r epa n dq` are real, then `(p ,q)=(______,_____)` .

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Fill in the blanks The coefficient of x^(99) in the polynomial (x-1)...

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  2. Let z1, z2, z3 be three complex numbers and a ,b ,c be real numbers no...

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  3. Fill in the blanks If 2+isqrt(3) is a root of the equation x^2+p x+q=0...

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  4. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

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  5. Fill in the blanks. If the product of the roots of the equation x^2-3k...

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  6. Solve for z : z^2-(3-2i)z=(5i-5)dot

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  7. If the equations x^2+ax+b=0 and x^2+bx+a=0 have one common root. Then ...

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

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

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

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

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

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

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

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

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

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  19. Column I, Column II y=(x^2-2x+4)/(x^2+2x+4),x in R ,t h e ny c a n...

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

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