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Simplify: (sqrt(5+12 i)+sqrt(5-12 i))/(s...

Simplify: `(sqrt(5+12 i)+sqrt(5-12 i))/(sqrt(5+12 i)-sqrt(5-12 i))`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If one root of the equation z^2-a z+a-1= 0 is (1+i), where a i...

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  2. If |z1|=|z2|=|z3|=1 and z1+z2+z3=0 then the area of the triangle whose...

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  3. Simplify: (sqrt(5+12 i)+sqrt(5-12 i))/(sqrt(5+12 i)-sqrt(5-12 i))

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  4. Find a quadratic equation whose product of roots x1 and x2 is equa...

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  5. If sqrt(5-12 i)+sqrt(-5-12 i)=z , then principal value of a rgz can be

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  6. If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

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  7. If a and b(!=0) are the roots of the equation x^2+a x+b=0, then find...

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  8. Let A ,B ,C ,D be four concyclic points in order in which A D : A B=C ...

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  9. Convert (1+3i)/(1-2i) into the polar form.

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  10. If the sum of the roots of the equation (a+1)x^2+(2a+3)x+(3a+4)=0 is ...

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  11. Let the altitudes from the vertices A, B and C of the triangle ABC me...

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  12. For |z-1|=1, show that tan{[a r g(z-1)]/2}-((2i)/z)=-i

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  13. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

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  14. If z1=9y^2-4-10ix,z2=8y^2-20i where z1=barz2 then z=x+iy is equal to

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  15. If a rg(z1)=170^0 and arg(z2)=70^0 , then find the principal argument...

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  16. z1, z2 and z3 are the vertices of an isosceles triangle in anticlockwi...

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  17. function f , x ->R , f(x) = (3x^2+mx+n)/(x^2+1) , if the range of func...

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  18. If z(1) and z(2) are conjugate to each other , find the principal argu...

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  19. If a is a complex number such that |a|=1, then find the value of a, s...

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  20. If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=...

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