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Let z1 \and\ z2 be the roots of the equa...

Let `z_1 \and\ z_2` be the roots of the equation `z^2+p z+q=0,` where the coefficients `p \and \q` may be complex numbers. Let `A \and\ B` represent `z_1 \and\ z_2` in the complex plane, respectively. If `/_A O B=theta!=0 \and \O A=O B ,\where\ O` is the origin, prove that `p^2=4q"cos"^2(theta//2)dot`

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The correct Answer is:
` rArr p^(2) = 4 q cos^(2)alpha //2 `
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VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
  1. If |z|<=1,|w|<=1, then show that |z- w|^2<=(|z|-|w|)^2+(argz-argw)^2

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  2. Find the non-zero complex number z satisfying z =i z^2dot

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  3. Let z1 \and\ z2 be the roots of the equation z^2+p z+q=0, where the co...

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  4. Let barz+bbarz=c,b!=0 be a line the complex plane, where bar b is the ...

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  5. If z(1) and z(2) are two complex numbers such that |z(1)| lt 1 lt |z...

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  6. about to only mathematics

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  7. Let A={theta in (-pi /2,pi):(3+2i sin theta )/(1-2 i sin theta ) is pu...

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  8. Let Z0 is the root of equation x^2+x+1=0 and Z=3+6i(Z0)^(81)-3i(Z0)^(9...

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  9. If z=((sqrt3)/(2)+(1)/(2)i)^5+((sqrt3)/(2)-(i)/(2))^5, then (a)...

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  10. Let (-2-(1)/(3)i)^(3) = (x+iy)/(27) (i=sqrt(-1)), where x and y are re...

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  11. Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) T...

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  12. If (x-alpha)/(z+alpha)(alpha in R) is a purely imaginery number and |z...

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  13. Let Z(1) and Z(2) be two complex numbers satisfying |Z(1)|=9 and |Z(2)...

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  14. if z = (sqrt 3 ) /(2) + (i)/(2) ( i=sqrt ( -1) ), then ( 1 + ...

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  15. All the points in the set S={(alpha+i)/(alpha-i):alpha in R } (i= sqrt...

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  16. Let z in c be such that |z| lt . If omega = (5 + 3z)/(5(1 - z)), then ...

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  17. If z = ((1+i)^(2))/(alpha-i), alpha in R has magnitude sqrt((2)/(5)) ...

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  18. Let Z and w be two complex number such that |zw|=1 and arg(z)−arg(w)=p...

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  19. The equation |z-1|=|z+1|,i= sqrt(-1)represents =

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  20. if (2z-n)/(2z+n)=2i-1,n in N in N and IM(z)=10, then

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