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

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

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If z_1a n dz_2 both satisfy z+barz r =2|z-1| and a r g(z_1-z_2)=pi/4 , then find I m(z_1+z_2) .

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the sum of the roots of the equation (a+1)x^2+(2a+3)x+(3a+4)=0 is ...

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  2. Let the altitudes from the vertices A, B and Cof the triangle e ABCmee...

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

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

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  5. If z1=9y^2-4-10ix, z2=8y^2-20i, where z1=overline z2, then find z=x+i...

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

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

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

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

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

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  11. 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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  12. Find the value of expression (cospi/2+i sin(pi/2))(cos(pi/(2^2))+i si...

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  13. Solve for z , i.e. find all complex numbers z which satisfy |z|^2-2i z...

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  14. If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' a...

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  15. If a ,b are complex numbers and one of the roots of the equation x^2+a...

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  16. If |z1|=|z2|=1, then prove that |z1+z2|= |1/z1+1/z2∣

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  17. If (a x^2+c)y+(a^(prime)x^2+c^(prime) )=0 and x is a rational function...

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  18. Find the principal argument of the complex number sin(6pi)/5+i(1+cos(6...

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  19. For x in (0,1) , prove that i^(2i+3) ln((i^3x^2+2x+i)/(i x^2+2x+i^3))=...

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  20. The sum of the non-real root of (x^2+x-2)(x^2+x-3)=12 is -1 b. 1 c. -...

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