What is the complex number formula? Do 12th-grade students in Vietnam have the right to receive comprehensive education with fairness?

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What is the complex number formula? Do 12th-grade students in Vietnam have the right to receive comprehensive education with fairness?

What is the complex number formula?

12th-grade students in Vietnam can refer to the following information on complex number formula:

What is the complex number formula?

Definition of Complex Numbers

A complex number is an extension of a real number, represented as:

z = a + bi

Where:

a is the real part of the complex number (a real number)

b is the imaginary part of the complex number (a real number)

i is the imaginary unit, satisfying i^2 = -1

Example:

2 + 3i is a complex number with a real part of 2 and an imaginary part of 3.

-5i is a complex number with a real part of 0 and an imaginary part of -5.

Geometric Representation of Complex Numbers

The complex number z = a + bi can be represented on the complex plane (the Oxy plane), where:

The horizontal axis (Ox) represents the real part a

The vertical axis (Oy) represents the imaginary part b

The point M(a, b) represents the complex number z

Operations with Complex Numbers

Addition, subtraction:

(a + bi) + (c + di) = (a + c) + (b + d)i

(a + bi) - (c + di) = (a - c) + (b - d)i

Multiplication:

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

Division:

(a + bi) / (c + di) = [(ac + bd) / (c^2 + d^2)] + [(bc - ad) / (c^2 + d^2)]i with the condition c^2 + d^2 ≠ 0

Conjugate of a Complex Number

The conjugate of a complex number z = a + bi is z' = a - bi.

Properties:

z.z' = a^2 + b^2 (a real number)

z + z' = 2a (double the real part of z)

Modulus of a Complex Number

The modulus of the complex number z = a + bi is the length of the line segment OM on the complex plane and is calculated by:

|z| = √(a^2 + b^2)

Trigonometric Form of a Complex Number

The complex number z can be written in trigonometric form:

z = r(cosφ + isinφ)

Where:

r = is the modulus of z

φ is the argument of z, the angle formed by the positive Ox ray and the line OM

Euler's Formula:

e^(iφ) = cosφ + isinφ

Thanks to Euler's formula, we can write the complex number z in exponential form:

z = re^(iφ)

Applications of Complex Numbers

Complex numbers have important applications in fields such as:

Electronics: Describing alternating currents, and alternating circuit analyses.

Quantum Physics: Describing fundamental particles.

Signal Processing: Fourier analysis.

Computer Graphics: Representing geometric transformations.

Note: The information is for reference only.

What is the Complex Number Formula? Are the rights of 12th-grade students at school equal in enjoying a comprehensive education?

What is the complex number formula? Do 12th-grade students in Vietnam have the right to receive comprehensive education with fairness? (Image from the Internet)

What are the regulations on assessing the training results of 12th-grade students in the 2024-2025 school year?

Specifically, according to clause 2 Article 8 of Circular 22/2021/TT-BGDDT, the training results of 12th-grade students in each semester and in the entire school year shall be assessed by one of 4 categories: Excellent, Good, Qualified, Unqualified.

1) Training results of students in each semester

- Excellent: Satisfy requirements for traits under formal education program excellently and display merits.

- Good: Satisfy requirements for traits under formal education program well and display merits but not enough to be placed in Excellent category.

- Qualified: Satisfy requirements for traits under formal education program.

- Unqualified: Fail to satisfy requirements for traits under formal education program.

2) Training results of students in the entire school year

- Excellent: a student is placed in Excellent category in the 2nd semester and in Good category or higher in the 1st semester.

- Good: a student is placed in Good category in the 2nd semester and Qualified category or higher in the 1st semester; or Qualified category in the 2nd semester and Good category in the 1st semester; or Good category in the 2nd semester and Qualified category or Unqualified category in the 1st semester.

- Qualified: a student is placed in Qualified category in the 2nd semester and Good, Qualified, or Unqualified category in the 1st category; or Good category in the 2nd semester and Unqualified in the 1st semester.

- Unqualified: other cases.

Do 12th-grade students in Vietnam have the right to receive comprehensive education with fairness?

The rights of 12th-grade students are specifically stipulated in Article 35 of the lower secondary school, upper secondary school and multi-level school charter issued with Circular 32/2020/TT-BGDDT as follows:

- Receive comprehensive education with fairness, be provided with time, facilities, hygiene and safety to learn in class and self-learn at home, be informed of their education and training, and be able to use learning, cultural and sport equipment of their schools as per the law.

- Receive respect, protection and fair and democratic treatment, complain to their schools and education authorities about decisions concerning themselves; transfer school with legitimate reason as per existing regulations; enter school before the compulsory starting age, skip a grade and study at an age higher than the compulsory attendance age according to regulations in Article 33 of Circular 32/2020/TT-BGDDT.

- Participate in activities for development of their gifts in academic subjects, sports and art organized by their schools if able to.

- Students eligible for social benefits, disadvantaged students and gifted students may receive sponsorship or other benefits as per the law.

- Transfer school if eligible according to regulations following school transfer procedures stipulated by the Minister of Education and Training.

- Enjoy other rights as per the law.

Thus, 12th-grade students at school will receive comprehensive education with fairness.

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