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Given that the complex numbers which sat...

Given that the complex numbers which satisfy the equation `| z bar z ^3|+| bar z z^3|=350` form a rectangle in the Argand plane with the length of its diagonal having an integral number of units, then area of rectangle is 48 sq. units if `z_1, z_2, z_3, z_4` are vertices of rectangle, then `z_1+z_2+z_3+z_4=0` rectangle is symmetrical about the real axis `a r g(z_1-z_3)=pi/4or(3pi)/4`

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let z1, z2, z3 be the three nonzero complex numbers such that z2!=1,a=...

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  2. If tantheta and sectheta are the roots of a x^2+b x+c=0, then prove th...

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  3. Given that the complex numbers which satisfy the equation | z bar z ^...

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  4. If the roots of the equation x^2-b x+c=0 are two consecutive integers,...

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  5. If the difference between the roots of the equation x^2+""a x""+""1...

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  6. For what real values of a do the roots of the equation x^2-2x-(a^2-1)=...

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  7. If P and Q are represented by the complex numbers z1 and z2 such that ...

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  8. Find the value of a for which the equation a sin(x+pi/4)=sin2x+9...

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  9. Given z=f(x)+ig(x) where f,g:(0,1) to (0,1) are real valued functions....

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  10. Let a ,b and c be real numbers such that a+2b+c=4 . Find the maximum v...

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  11. If z=x+i y , then the equation |(2z-i)/(z+1)|=m does not represents a ...

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  12. Prove that for real values of x ,(a x^2+3x-4)//(3x-4x^2+a) may have a...

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  13. Given that the two curves a r g(z)=pi/6 and |z-2sqrt(3)i|=r intersect ...

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  14. Let x^2-(m-3)x+m=0 (m epsilon R) be a quadratic equation . Find the va...

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  15. A particle P starts from the point z0=1+2i , where i=sqrt(-1) . It ...

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  16. Prove that for all real values of x and y ,x^2+2x y+3y^2-6x-2ygeq-11.

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  17. Let z=x+i y be a complex number where xa n dy are integers. Then, the ...

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  18. The values of 'a' for which the equation (x^2 + x + 2)^2 - ( a-3)( x^2...

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  19. A man walks a distance of 3 units from the origin towards the North-...

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  20. Find the values of a for whilch the equation sin^4x+asin^2x+1=0 will h...

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