Physical Meaning of Multiplication of Complex Numbers, What Does Multiplication of Complex Numbers M

Complex numbers are useful for studying physical problems. But the force work is obviously the opposite of addition and subtraction, which is not right. The most used place is the wave.

For example, the most common one-dimensional mechanical wave, the phase can be written in the form of e (wt-kx), which can be taken apart to represent the contribution of time and coordinates to the phase. Complex numbers have the form of exponential functions, and since exponential functions are much better mathematically than trigonometric functions, complex numbers are generally used for everything involving waves.

Complex numbers are actually a kind of number that is thought to be defined, and the expression is x=a+bi, where i is the sign of a complex number (of course, it is not also a complex number, but it will also be classified as a real number), thus constituting a complex plane. That is to say, each complex number has a unique point corresponding to it in the complex plane, which is equivalent to a vector, the starting point is the origin point, the end point is the complex number point, and has its own modulus, that is, the length of the vector line segment.

The operation of squares (or multiplication) of complex numbers is the multiplication of an term of ordinary algebraic formulas, and it is treated as vectors. If, as you say, "Like the square of a complex number, geometrically it is the square of the vector from that point to the origin on a complex plane." "It's just that the length of the modulus becomes the original square, but there are an infinite number of such points in the complex plane (draw circles centered on the origin), but the complex number is a vector and has directions.

When the vectors are multiplied, the direction changes. Your kind of "vector squared is just the square of the real part plus the square of the imaginary real number." "It's wrong, you can verify it with a very simple example.

At the end of the day, complex arithmetic is the same as vector arithmetic!

Oh, and I'm referring to the same algorithm, but the final result of the complex number depends on the situation, it may be a complex number or a real number. Attachment is a special kind of vector that can only be applied in complex planes, not general spatial vectors.

Multiplication of complex numbers: Multiply two complex numbers, similar to twoPolynomialsMultiply, i2=-1 in the result, merge the real part and the imaginary part separately. The product of two complex numbers is still a complex number.

The earliest literature on the plural roots of the broad calendar is from the Greek mathematician Helen in the first century AD.

He considered the impossibility of flat-topped pyramids.

Complex numbers: We call numbers that are shaped like ridges and z=a+bi (both a and b are real) complex numbers. Where, a is called the real part, b is called the imaginary part, and i is called the imaginary unit.

When the imaginary part of z is b 0, then z is a real number; When the imaginary part of z is b≠0 and the real part is 0, z is often called a pure imaginary number. The complex cherry blossom target is an algebraic closure of the real number field, i.e., any complex coefficient polynomial always has roots in the complex number field. The plural is made by Milan, Italy.

First introduced by the scholar Cardan in the 16th century, the concept gradually became accepted by mathematicians.