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Multiplication and division formula of complex numbers
The multiplication and division formula of complex numbers is: (a+bi) (c+di) = (AC-BD)+(BC+AD) i; (a+bi)/(c+di)=(AC+BD)/(C2+D2)+((BC-ad)/(C2+D2))I .

1, where a is called the real part, b is called the imaginary part, and I is called the imaginary part. When the imaginary part of z is equal to zero, z is often called a real number; When the imaginary part of z is not equal to zero and the real part is equal to zero, z is often called pure imaginary number.

2. Complex number field is an algebraic closure of real number field, that is, any polynomial with complex coefficients always has roots in complex number field. Complex number was first put forward by Cardan, a scholar in Milan, Italy, in the16th century. Through the work of D'Alembert, De Moivre, Euler and Gauss, this concept was gradually accepted by mathematicians.

3. Complex number algorithm includes addition, subtraction, multiplication and division. The sum of two complex numbers is still a complex number, its real part is the sum of the real parts of the original two complex numbers, and its imaginary part is the sum of the original two imaginary parts. The addition of complex numbers satisfies the commutative law and associative law.

4. When a complex number is used as the base, exponent and real number of power and logarithm, its operation rules can be derived from Euler formula e i θ = cos θ+isinθ (arc system).

The methods and skills of learning mathematics are as follows:

1, get into the habit of previewing.

Because you learn what the teacher wants to say in advance, you will know what you can't do, and you will have a focus when you learn. Of course, it would be better if you taught yourself completely.

2. Follow the book to do exercises

Preview is not an end. If you have time, you can do examples and exercises after class and check the preview. If you can explain everything, you can learn it. Even if you can't, you can listen to the teacher again.

3. Do the homework assigned by the teacher and do it carefully.

When you do it, you can write the problem-solving process directly next to the topic, such as multiple-choice questions and fill-in-the-blank questions, because there are many blanks to write in the solution. The advantage of this is that the teacher can keep up with the ideas when talking about the topic, and it is not easy to get distracted.

Step 4 sort out the wrong questions

After every exam, there are always many wrong questions. For these questions, don't think that you will do them if you understand them in class. It's easier to see flowers than to embroider. You will know if you can do it yourself. Moreover, we should refer to the wrong questions in the reference book and re-learn the knowledge.