Imaginary number:
An imaginary number can refer to an imaginary number or a number that does not represent a specific quantity. In mathematics, imaginary numbers are numbers in the form of a+b*i, where a and b are real numbers, b≠0, i? = - 1。 The word imaginary number was founded by Descartes, a famous mathematician in the17th century, because the concept at that time thought it was a non-existent real number. Later, it was found that the real part A of the imaginary number a+b*i can correspond to the imaginary part B of the horizontal axis on the plane and the vertical axis on the plane, so that the imaginary number a+b*i can correspond to the points (a, b) on the plane.
Basic operation:
Addition and subtraction are the same as real numbers (a+bi).
Power (screen) (A+Bi) n = r n ∠ nθ, power is the same as real number operation, but (A+Bi) n is inconvenient to operate, so it is generally converted into r n ∠ nθ and then back to (A+Bi) to simplify the operation.
Multiplication, like real numbers, can be accelerated by "the square of I =- 1, the cube of I =-i, and the fourth power of I = 1". Multiplication can also be transformed (generally not used), that is, (A+Bi)(A+Bi)= rR∞(θ 1+θ2).
Division and real number are the same in meaning (just the inverse operation of multiplication), but "(A+Bi)/(a+bi)=C+Di" belongs to a binary linear equation, although there are formulas c = (aa+bb)/(a 2+b 2) and d = (ab-ab)/(a 2). Unless the divisor is a real number, it is generally converted, that is, (A+Bi)/(A+Bi)= R/R∞(θ 1-θ2).
The absolute value indicates the distance from the origin, not the sign, so ABS (a+bi) = r = √ (a 2+b 2).
If the square root and the cube root are the inverse operations of a cube, then the transformation is enough if there is a square root of (a+bi) = (a+bi) (1/n) = r (1/n) ≈ θ/n.