Source of knowledge point definition &; Explanation:
The imaginary unit I is a special number in mathematics, which was introduced to solve the problem that the equation X 2 =- 1 in the real number system cannot be satisfied. By defining I 2 =- 1, we can introduce imaginary unit I to represent the square root of negative numbers.
Application of knowledge points:
Imaginary unit I is widely used in mathematics. It is one of the foundations of complex system, which is helpful to the representation and calculation of complex numbers. Complex number consists of real part and imaginary part, which can be expressed in the form of a+bi, where A represents real part, B represents imaginary part and I represents imaginary part. Imaginary unit I plays an important role in complex number operation, trigonometric function and complex plane.
Examples of knowledge points:
Example: Calculate the product of the following complex numbers: (2+3i)( 1+4i)
A: According to the rules of complex multiplication, the expansion calculation is as follows:
(2+3i)( 1+4 I)= 2 * 1+2 * 4 I+3i * 1+3i * 4 I
= 2 + 8i + 3i + 12i^2
Because I 2 =-1,we get:
(2+3i)( 1+4 I)= 2+8i+3i+ 12(- 1)
= 2 + 8i + 3i - 12
= - 10 + 1 1i
Therefore, (2+3i) (1+4i) =-10+1i.
Extended reading:
If you are interested in complex numbers and imaginary unit I, you can further explore the algorithm of complex numbers, Euler formula, geometric interpretation of complex numbers and so on. Understand the application of imaginary number in physics, engineering and calculation, such as impedance calculation, signal processing and quantum mechanics in AC circuits. Relevant mathematics textbooks and reference books provide more in-depth learning materials and examples.