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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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CENGAGE PUBLICATION-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 C of the triangle ABC me...

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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=barz2 then z=x+iy is equal to

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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 , x ->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 (cos(pi/2)+i sin(pi/2))(cos(pi/(2^2))+i s...

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

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

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

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

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  18. If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1....

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  19. The number of roots of the equation sqrt(x-2)(x^2-4x+3)=0 is (A) Th...

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  20. If z1,z2 and z3,z4 are two pairs of conjugate complex numbers, then ar...

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