Online Test — Complex Numbers and Quadratic Equations
10 Questions • 20 min • Chapter MCQ
20:00
Question 1 of 10
easy
Find the modulus of (1 + i√3)/(1 - i√3).
1
2
3
4
Explanation: The modulus of the numerator is √(1+3)=2. The modulus of the denominator is √(1+3)=2. The ratio is 2/2 = 1.
Question 2 of 10
medium
The argument of 1 + i is:
45°
90°
30°
60°
Explanation: tan θ = 1.
Question 3 of 10
easy
(1 + i)(1 − i) equals:
2
0
1
−2
Explanation: 1 − i² = 2.
Question 4 of 10
easy
The imaginary part of 5 − 7i is:
−7
7
5
−5
Explanation: The coefficient of i is −7.
Question 5 of 10
medium
Expand and simplify (1-i)⁴.
4
-4
4i
-4i
Explanation: (1-i)⁴ = ((1-i)²)² = (1 - 2i + i²)² = (-2i)² = 4i² = -4.
Question 6 of 10
medium
Find the multiplicative inverse of 3 - 4i.
(3+4i)/25
(3-4i)/25
3+4i
1/(3+4i)
Explanation: Inverse = 1/(3-4i). Multiply numerator and denominator by 3+4i to get (3+4i)/(9+16) = (3+4i)/25.
Question 7 of 10
medium
For z = a + bi, z − z̄ equals:
2bi
2a
a + b
0
Explanation: Real parts cancel.
Question 8 of 10
easy
The real part of 5 − 7i is:
5
−7
7
−5
Explanation: The real part is 5.
Question 9 of 10
easy
If z = 0 + 9i, then z is:
Purely imaginary
Purely real
Neither
Complex with real part 9
Explanation: Real part is zero.
Question 10 of 10
medium
The modulus of −5 + 12i is:
13
17
7
169
Explanation: √(25 + 144) = 13.