Complex Number and Quadratic Equations Quiz-22

Complex numbers and quadratic equations is a segment of maths that deals with crucial theorems and concepts along with various formulae. It comprises of linear and quadratic equations along with roots related to the complex number's set (known as complex roots)..

Q1.  If |z-1|≤2 and |Ï‰z-1-Ï‰2 |=a (where Ï‰ is a cube root of unity) then complete set of values of a is
•  0≤a≤2
•  1/2≤a≤√3/2
•  √3/2-1/2≤a≤1/2+√3/2
•  0≤a≤4
Solution
Q2. If Î±,Î² are real and Î±2,Î²2 are the roots of the equation a2 x2+x+1-a2=0(a>1), then Î²2=
•  a2
•  1-1/a2
•  1-a2
•  1+a2
Solution

Q3. If the complex number z satisfies the condition |z|≥3, then the least value of [z+(1/z)| is equal to
•  5/3
•  8/3
•  11/3
•  None of these
Solution

Q4. The points z1=3+√3 i and z2=2√3+6i are given on a complex plane. The complex number lying on the bisector of the angle formed by the vectors z1 and z2 is
•  z=((3+2√3))/2+(√3+2)/2 i
•  z=5+5i
•  z=-1-i
•  None of these
Solution

Q5. If |z2-3|=3|z| then the maximum value of |z| is
•  1
•  (3+√21)/2
•  (√21-3)/2
•  None of these
Solution

Q6. If a complex number z satisfies |2z+10+10i|≤5√3-5, then the least principle argument of z is
•  -5Ï€/6
•  -11Ï€/12
• -3Ï€/4
•  -2Ï€/3
Solution

Q7. If x be real, then x/(x2-5x+9) lies between
•  -1 and -1/11
•  1 and -1/11
•  1 and 1/11
•  None of these
Solution

Q8. The complex number associated with the vertices A,B,C of ∆ABC are eth,Ï‰,¯Ï‰, respectively [where Ï‰,¯Ï‰ are the complex cube roots of unity and cos⁡Î¸>Re(Ï‰)], then the complex number of the point where angle bisector of A meets the circumcircle of the triangle, is
•  eiÎ¸
•  e(-iÎ¸)
•  Ï‰¯Ï‰
•  Ï‰+¯Ï‰
Solution

Q9.  If arg⁡((z1-z/|z| )/(z/|z| ))=Ï€/2 and |z/|z| -z1 |=3 then |z1 | equals to
•  √26
•  √10
•  √3
•  2√2
Solution
Q10. Dividing f(z) by z-i, we obtain the remainder i and dividing it by z+i, we get the remainder 1+i, then remainder upon the division of f(z) by z2+1 is
•  1/2 (z+1)+i
•  1/2 (iz+1)+i
•  1/2 (iz-1)+i
• 1/2 (z+i)+1
Solution

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