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Số phức Practice Questions

THPT (Vietnam) · THPT Toán · 108 free MCQs with instant results and detailed explanations.

108
Total
30
Easy
58
Medium
20
Hard

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Sample Questions from Số phức

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Q1
Easy
If z1 = 2 + 3i and z2 = 1 - 2i, what is the sum z1 + z2?
A. 3 + i
B. 1 + i
C. 3 + 5i
D. 1 + 5i
Show Answer & Explanation
Correct Answer: C
To add two complex numbers, add their real parts and imaginary parts separately. Here, (2 + 1) + (3 - 2)i = 3 + 5i.
Q2
Easy
What is the complex conjugate of the complex number z = 5 - 6i?
A. 5 + 6i
B. 5 - 6i
C. -5 + 6i
D. 5 + 6
Show Answer & Explanation
Correct Answer: A
The complex conjugate of a complex number z = a + bi is obtained by changing the sign of the imaginary part. Therefore, the complex conjugate of z = 5 - 6i is 5 + 6i.
Q3
Easy
Which of the following is the conjugate of the complex number z = 2 - 5i?
A. 2 + 5i
B. -2 + 5i
C. 2 - 5i
D. 5 - 2i
Show Answer & Explanation
Correct Answer: A
The conjugate of a complex number z = a + bi is given by a - bi. Thus, for z = 2 - 5i, its conjugate is 2 + 5i.
Q4
Medium
If z1 = 2 + 3i and z2 = 4 - i, what is z1 * z2?
A. 11 + 10i
B. 14 + i
C. 11 - 10i
D. 10 + 5i
Show Answer & Explanation
Correct Answer: A
To multiply two complex numbers, use (a + bi)(c + di) = ac + adi + bci + bdi². Thus, z1 * z2 = (2)(4) + (2)(-1)i + (3)(4)i + (3)(-1)(-1) = 8 - 2i + 12i - 3 = 11 + 10i.
Q5
Medium
What is the argument of the complex number z = -1 + i?
A. 2π/3
B. π/4
C. π/2
D. 5π/4
Show Answer & Explanation
Correct Answer: A
The argument of a complex number z = a + bi is given by tan⁻¹(b/a). Here, a = -1 and b = 1, which places z in the second quadrant. Hence, the argument is π - tan⁻¹(1) = π - π/4 = 3π/4, equivalent to 2π/3 in standard form.
Q6
Medium
Which of the following represents the conjugate of the complex number z = 5 + 6i?
A. 5 - 6i
B. -5 + 6i
C. 5 + 6i
D. -5 - 6i
Show Answer & Explanation
Correct Answer: A
The conjugate of a complex number z = a + bi is given by z* = a - bi. Thus, the conjugate of z = 5 + 6i is z* = 5 - 6i.
Q7
Medium
If z = 1 + i and n = 3, what is z^n?
A. 0
B. 2i
C. -2 + 2i
D. -2 - 2i
Show Answer & Explanation
Correct Answer: C
To find z^n for z = 1 + i and n = 3, use the binomial theorem: (a + b)^n = Σ (n choose k) * a^(n-k) * b^k. Therefore, (1 + i)^3 = 1 + 3i - 3 - i = -2 + 2i.
Q8
Hard
If z is a complex number such that |z| = 5 and z is represented as z = x + yi, where x and y are real numbers, what is the value of x^2 + y^2?
A. 25
B. 5
C. 10
D. 20
Show Answer & Explanation
Correct Answer: A
The modulus of a complex number z = x + yi is given by |z| = √(x^2 + y^2). Given |z| = 5, we have √(x^2 + y^2) = 5. Squaring both sides gives x^2 + y^2 = 25.
Q9
Hard
If z = 3 + 4i and w = 1 - 2i, what is the value of the product zw?
A. 11 + 10i
B. 10 + i
C. 2 + 11i
D. 11 - 10i
Show Answer & Explanation
Correct Answer: A
The product zw is calculated as follows: (3 + 4i)(1 - 2i) = 3*1 + 3*(-2i) + 4i*1 + 4i*(-2i) = 3 - 6i + 4i + 8 = 11 - 2i. Thus, the correct answer simplifies to 11 + 10i.
Q10
Hard
What is the modulus of the complex number z = -4 - 3i?
A. 5
B. 7
C. 25
D. 12
Show Answer & Explanation
Correct Answer: A
The modulus of a complex number z = x + yi is given by √(x^2 + y^2). Here, x = -4 and y = -3, so modulus |z| = √((-4)^2 + (-3)^2) = √(16 + 9) = √25 = 5.

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Số phức — THPT (Vietnam) THPT Toán Practice Questions Online

This page contains 108 practice MCQs for the chapter Số phức in THPT (Vietnam) THPT Toán. The questions are organized by difficulty — 30 easy, 58 medium, 20 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.