Cách tìm môđun của số phức cực hay, chi tiết – Toán lớp 12

Kiến Thức Y Khoa 25/08/2023

149 2 minutes read

Table of Contents

Introduction

Welcome to Kienthucykhoa.com! In this article, we will dive into the topic of finding the modulus of complex numbers. Whether you are a student or just interested in mathematics, understanding this concept is essential. So let’s get started!

Modulus of Complex Numbers

The modulus of a complex number, denoted as |z|, is the distance between the origin and the point z in the complex plane. It represents the magnitude or absolute value of the complex number.

Method

To find the modulus of a complex number z, follow these steps:

Square the real part of z and the imaginary part of z.
Add these squared values together.
Take the square root of the sum obtained.

For any complex number z ∈ C, we have the following result:

|z| = √(x^2 + y^2)

Illustrative Examples

Now, let’s explore some examples to grasp the concept better.

Example 1:

Find the complex numbers z that satisfy the following:
A. z1 = -1 + i; z2 = 1 – i
B. z1 = 1 + i; z2 = -1 – i
C. z1 = -1 + i; z2 = -1 – i
D. z1 = 1 + i; z2 = 1 – i

Solution:
We need to find the values of x and y that satisfy x^2 + y^2 = 2.
Therefore, we can choose option D.

Example 2:

Given the complex number z = 2 – 3i, calculate |z|.

Solution:
The modulus of z can be calculated as follows:
|z| = √(2^2 + (-3)^2)
Choosing option C, we have |z| = √13.

Example 3:

Consider two complex numbers z1 = 1 + 3i and z2 = 2 – i. Find P = |z1 + z2|.

Solution:
We can find the modulus of the sum of z1 and z2:
z1 + z2 = (1 + 3i) + (2 – i) = 3 + 2i
|z1 + z2| = √((3^2) + (2^2))
Choosing option D, we get P = √13.

Conclusion

In this article, we explored how to find the modulus of complex numbers. Remember, the modulus represents the magnitude or absolute value of a complex number. By applying the steps mentioned earlier, you can easily calculate the modulus. So the next time you encounter a complex number, you will be confident in determining its modulus.

For more comprehensive lessons and exercises on complex numbers and other mathematical topics, visit Kienthucykhoa.com.

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