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let z1=10+6i and z2=4+6i if z is nay com...

let `z_1=10+6i` and `z_2=4+6i` if z is nay complex number such that argument of `(z-z_1)/(z-z_2)` is `pi/4` the prove that `abs(z-7-9i)=3sqrt2`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Show that the equation of a circle passing through the origin and ha...

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  2. The function f(x)=a x^3+b x^2+c x+d has three positive roots. If the ...

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  3. let z1=10+6i and z2=4+6i if z is nay complex number such that argument...

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  4. Let vertices of an acute-angled triangle are A(z1),B(z2),a n dC(z3)dot...

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  5. If (18x^2+12x+4)^n = a0 +a(1x)+ a(2x)^2 +......+ a(2n)x^(2n), prove th...

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  6. If z=z0+A( bar z -( bar z 0)), w h e r eA is a constant, then prove t...

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  7. If (sinalpha)x^2-2x+bgeq2 for all real values of xlt=1a n dalpha in (0...

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  8. If z1, z2, z3 are three complex numbers such that 5z1-13 z2+8z3=0, t...

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  9. If one root x^2-x-k=0 is square of the other, then k= a.2+-sqrt(5)...

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  10. If z1, z2 are complex number such that (2z1)/(3z2) is purely imaginary...

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  11. If alpha,a n dbeta be the roots of the equation x^2+p x-1//2p^2=0,w h ...

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  12. If z1,z2,z3 are complex numbers such that 2/z1=1/z2 + 1/z3, show that ...

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  13. Find the range of f(x)(x^2-x+1)/(x^2+x+1)

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  14. If ((3-z1)/(2-z1))((2-z2)/(3-z2))=k(k >0) , then prove that points A(z...

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  15. x^2-x y+y^2-4x-4y+16=0 represents a. a point b. a circle c. ...

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  16. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

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  17. If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta^...

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  18. Find real theta such that (3+2isintheta)/(1-2isintheta) is purely real...

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  19. If the roots of the equation a x^2+b x+c=0 are of the form (k+1)/k and...

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  20. Prove that tan(iloge((a-ib)/(a+ib)))=(2ab)/(a^2-b^2) (where a, b in ...

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