## Complex Number and Quadratic Equations Quiz-21

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.  The maximum area of the triangle formed by the complex coordinate z,z1,z2 which satisfy the relations |z-z1 |=|z-z2 | and |z-(z1+z2)/2|≤r, where r>|z1-z2 | is
•  1/2 |z1-z2 |2
•  1/2 |z1-z2 | r
•  1/2 |z1-z2 |2 r2
•  1/2 |z1-z2 | r2
Solution
Q2. The points z1,z2,z3,z4 in the complex plane are the vertices of a parallelogram taken in order if and only if
•  z1+z4=z2+z3
•  z1+z3=z2+z4
•  z1+z2=z3+z4
•  None of these
Solution

Q3. The equation √(x+1)-√(x-1)=√(4x-1) has
•  No solution
•  One solution
•  Two solutions
•  More than two solutions
Solution

Q4. If (b2-4ac)2 (1+4a2 )<64a2,a<0, then maximum value of quadratic expression ax2+bx+c is always less than
•  0
•  2
•  -1
•  -2
Solution

Q5. The curve y=(Î»+1) x2+2 intersects the curve y=Î»x+3 in exactly one point, if Î» equals
•  {-2,2}
•  {1}
•  {-2}
•  {2}
Solution

Q6. If a2+b2=1,then (1+b+ia)/(1+b-ia)=
•  1
•  2
• b+ia
•  a+ib
Solution

Q7. If z1,z2,z3 are the vertices of an equilateral triangle ABC such that |z1-i|=|z2-i|=|z3-i|, then |z1+z2+z3 | equals to
•  3√3
•  √3
•  3
•  1/(3√3)
Solution

Q8. Let C1 and C2 are concentric circles of radius 1 and 8/3, respectively, having centre at (3, 0) on the Argand plane. If the complex number z satisfies the inequality log(1/3)⁡((|z-3|2+2)/(11|z-3|-2))>1 then
•  z lies outside C1 but inside C2
•  z lies inside of both C1 and C2
•  z lies outside both of C1 and C2
•  None of these
Solution

Q9.  If a,b and c are real numbers such that a2+b2+c2=1, then ab+bc+ca lies in the interval
•  [1/2,2]
•  [-1,2]
•  [-1/2,1]
•  [-1,1/2]
Solution
Q10. If z=x+iy and x2+y2=16, then the range of |(|x|-|y|)| is
•  [0,4]
•  [0,2]
•  [2,4]
• None of these
Solution

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