Complex Numbers and Quadratic Equations · Question 60

The number of values of z C, satisfying the equations |z-(4+8i)|= 10 and |z-(3+5i)|+|z-(5+11i)|=4 5, is :

1. 0
2. 2
3. 1
4. 4

Let e1 and e2 be two distinct roots of the equation x2-ax+2=0. Let the sets \a R : e1 and e2 are the eccentricities of hyperbolas\=( , ), and \a R : e1 and e2 are the eccentricities of an ellipse and a hyperbola, respectively\=( , ). Then 2+ 2+ 2 is equal to :

1. 18
2. 22
3. 26
4. 34

Let the set of all values of k R such that the equation z ( z+2+i )+k(2+3i)=0, z C, has at least one solution, be the interval [ , ]. Then 9( + ) is equal to :

1. -10
2. -8
3. 10 13
4. 8 13

Let S= \z C : z2+ 6 iz-3=0 \. Then z S z8 is equal to :

1. 162
2. 184
3. 262
4. 324

Let a, b C. Let , be the roots of the equation x2+ax+b=0. If - = 11 and 2- 2=3i 11, then ( 3- 3 )2 is equal to:

1. 160
2. 176
3. 194
4. 187

Let , be the roots of the equation x2-x+p=0 and , be the roots of the equation x2-4x+q=0; p, q Z. If , , , are in G.P., then |p+q| equals :

1. 16
2. 32
3. 34
4. 38

Let z1, z2 C be the distinct solutions of the equation z2+4z-(1+12i)=0. Then |z1|2+|z2|2 is equal to :

1. 18
2. 22
3. 29
4. 34

If the set of all solutions of |x2+x-9|=|x|+|x2-9| is [ , ] [ , ), then ( 2+ 2+ 2 ) is equal to:

1. 9
2. 18
3. 36
4. 72

Let z be a complex number such that |z+2|=|z-2| and ( z+3z-i )= 4. Then |z|2 is equal to:

1. 9
2. 4
3. 5
4. 1

Let S=\z C : z2+4z+16=0\. Then z S |z+ 3 i |2 is equal to :

1. 42
2. 23
3. 27
4. 38