Complex Numbers and Quadratic Equations

Let O be the origin, the point A be z1 = 3 + 2 2i, the point B(z2) be such that 3|z2| = |z1| and (z2) = (z1) + 6. Then

1. area of triangle ABO is 114
2. area of triangle ABO is 11 3
3. ABO is a scalene triangle
4. ABO is an obtuse angled isosceles triangle

If + i and + i are the roots of x2 - (3 - 2i)x - (2i - 2) = 0, i = -1, then + is equal to:

1. 2
2. -6
3. 6
4. -2

The product of all the rational roots of the equation (x2-9x+11)2-(x-4)(x-5)=3, is equal to

1. 7
2. 21
3. 28
4. 14

If and are the roots of the equation 2z2-3z-2i=0, where i= -1, then 16 ( 19+ 19+ 11+ 11 15+ 15 ) ( 19+ 19+ 11+ 11 15+ 15 ) is equal to

1. 441
2. 312
3. 409
4. 398

Let | z-i2 z+i |= 13, z C, be the equation of a circle with center at C. If the area of the triangle, whose vertices are at the points (0,0), C and ( ,0) is 11 square units, then 2 equals:

1. 12125
2. 100
3. 8125
4. 50

If the equation a(b-c)x2+b(c-a)x+c(a-b)=0 has equal roots, where a+c=15 and b= 365, then a2+c2 is equal to .

The number of complex numbers z, satisfying |z|=1 and | z z+ zz |=1, is :

1. 8
2. 10
3. 4
4. 6

Let , be the roots of the equation x2-ax-b=0 with Im( )<Im( ). Let Pn= n- n. If P3=-5 7 i, P4=-3 7 i, P5=11 7 i and P6=45 7 i, then | 4+ 4 | is equal to .

Let z1,z2 and z3 be three complex numbers on the circle |z|=1 with (z1)= - 4, (z2)=0 and (z3)= 4. If |z1 z2+z2 z3+z3 z1 |2= + 2, , Z, then the value of 2+ 2 is :

1. 41
2. 29
3. 24
4. 31

Let and be the distinct roots of 2x2+( )x-1=0, (0,2 ). If m and M are the minimum and the maximum values of 4+ 4, then 16(M+m) equals :

1. 27
2. 17
3. 25
4. 24