## Các số phức

Define:

A complex number $z$ is generally writen in the form: $z=a+bi$, where $a$ and $b$ are real numbers and $i$, called the imaginary unit, has the property that $i^2=-1$. The real numbers $a$ and$b$ are called the real and imaginary parts of $z=a+bi$ respectively.

Computing:

$a + bi = c + di \Leftrightarrow a = c,b = d$

Formulas for the addition, subtraction, multiplication, and division of complex number follow:

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

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

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

$\dfrac{{(a + bi)}}{{(c + di)}} = \dfrac{{(a + bi)}}{{(c + di)}}\dfrac{{(c - di)}}{{(c - di)}} = \dfrac{{ac + bd}}{{{c^2} + {d^2}}} + \left( {\dfrac{{bc - ad}}{{{c^2} + {d^2}}}} \right)i$

Note that the above operations are obtained by using the ordinary rules of algebra and replacing $i^2$ by $-1$ wherever it occurs

Hạnh phúc với những gì đang có
Bài này đã được đăng trong Học tiếng anh. Đánh dấu đường dẫn tĩnh.

### 2 Responses to Các số phức

1. Em xin dong gop mot bai tap tinh toan bang tieng anh de thay cung cac ban tham khao.Vua hoc toan vua nang cao kien thuc tieng anh:
Bai tap:
Cho x, y là số thực đảm bảo điều kiện 4 + = 1. Tìm giá trị lớn nhất và nhỏ nhất của biểu thức.

A = {2x+3y} / {2x+y+2}.
Exercise:
Based on the condition: 4 + = 1
The left side of this condition is always positive because:
4 and 0. Therefore, the above-mentioned condition is true when
(#) 4 =1 and = 0
(##) 4 =0 and = 1

From (#), with y=0 and 4=1, there will be two cases. (x = 0.5 and x = -0.5)
1) x=0.5 and y =0; ==> the value of the expression will be :
A = = =1/3

2)x=-0.5 and y =0; ==> the value of the expression will be :
A = = =-1

From (##), there will be two cases. (y =1 or y =-1)
3) x=0, y = 1; ==> the value of the expression will be :
A = = =1

4) x=0, y = -1; ==> the value of the expression will be:
A = = =-3

Conclusion:
– Comparing the results from 1), 2), 3), 4), the maximum value of the expression: A = = 1, when x=0 and y = 1; and the minimum value of the expression: A = = -3, when x=0 and y = -1.

2. dtphuong nói:

Cảm ơn em.