## Modulus of Complex Numbers MCQ Advance Level

Compared to other sections, mathematics is considered to be the most scoring section. If prepared thoroughly, mathematics can help students to secure a meritorious position in the exam. These questions are very important in achieving your success in Exams after 12th.

Q1. If z is a complex number, then the minimum value of | z | + | z – 1 | is

•  1
•  0
•  1/2
•  None of these

1

Q2. If |z+4|<=3, then the greatest and the least value of | z + 1 | are

•  6, – 6
•  6, 0
•  7, 2
•  0, – 1

6, 0

Q3. Let z be a complex number, then the equation z4+z+2=0 cannot have a root, such that

•  | z | < 1
•  | z | = 1
•  | z | > 1
•  None of these

| z | < 1

Q4. | z1 – 1 | < 1, | z2 – 2 | < 2, | z3 – 3 | < 3 then | z1 + z2 + z3 |

•  Is less than 6
•  Is more than 3
•  Is less than 12
•  Lies between 6 and 12

Is less than 12

Q5. The maximum value of | z | where z satisfies the condition |z+2/z|=2 is

•  √3 - 1
•  √3 + 1
•  √3
•  √2 + √3

√3 + 1

Q6. Let z and w be two complex numbers such that |z|<=1, |w|<=1 and |z+iw|=|z-iconj(w)|=2. Then z is equal to

•  1 or i
•  i or – i
•  1 or – 1
•  i or – 1

1 or – 1

Q7. If z1 and z2 be complex numbers such that z1 is not equal to z2 and |z1|=|z2|. If z1 has positive real part and z2 has negative imaginary part, then (z1+z2)/(z1-z2) may be

•  Purely imaginary
•  Real and positive
•  Real and negative
•  None of these

Purely imaginary

Q8. If z satisfies | z + 1 | < | z – 2 |, then w = 3z + 2 + i

•  | w + 1 | < | w – 8 |
•  | w + 1 | < | w – 7 |
•  w + conj(w)>7
•  | w + 5 | < | w – 4 |

| w + 1 | < | w – 8 |

Q9. If |z-4+3i|<=1 and m and n be the least and greatest values of | z | and K be the least value of (x4+x2+4)/x on the interval (0, ∞), then K =

•  n
•  m
•  m+n
•  None of these

n

Q10. The system of equations |z+1-i|=√2 and | z | = 3 has

•  No solution
•  One solution
•  Two solutions
•  None of these

No solution

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