Complex number: Complex number refers to the number A+Bi that can be written in the following form, where A and B are real numbers and I is imaginary unit (i.e.-1). When b=0 and z=a+ib=a+0, then the complex number becomes a real number;

When a=0 and z=a+bi=0+bi, we call it pure imaginary number.

Let z=a+bi be a complex number, then the complex number z' = a-bi is a * * yoke complex number of z 。

plural

The geometric form is represented by a plane rectangular coordinate system, and the coordinate system formed by taking X as the real axis, Y as the imaginary axis and O as the origin is called a complex plane.

Vector form: Vector form. The complex number z = a+bi is represented by the vector OZ, starting from the origin o and ending at the point Z(a, b).

Triangle. Complex number z = a+bi is transformed into triangular form.

z=r(cosθ+sinθi)

Where r = sqrt (A 2+B 2) is called the module (i.e. absolute value) of a complex number; θ is based on the x axis; The vector OZ is the angle of the terminal edge, which is called the radial angle of the complex number. This form is convenient for multiplication, division, power and root operations of complex numbers.

Exp(iθ) is used to replace cosθ+isθ in the triangular form Z = R(cosθ+isθ) of complex numbers, and the complex numbers are expressed in the exponential form Z = rexp (I θ).

Natural logarithm:

Also known as hyperbolic logarithm. Transcendental number [fc (] e =1+11! + 1/2! + 1/3! +… = 2.7 1828 … [fc] as the base logarithm. Use the symbol "l? N "means. There is a natural logarithm table to look up.

When X is close to positive infinity or negative infinity, the limit of [1+( 1/x)] X is equal to E, and actually E is discovered through this limit. It is an infinite acyclic decimal with a value of about 2.7 1828 1828. ...

Represented by e.

Logarithms based on e are usually used for.

E is a transcendental number.