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Imaginary number is a number whose square is negative. 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 imaginary number can correspond to the vertical axis on the plane, which is as real as the real number corresponding to the horizontal axis on the plane.
1777, the Swiss mathematician Euler (or translated as Euler) began to use the symbol i[ where i=√(- 1)] to represent the units of imaginary numbers. Later, people organically combined the imaginary number with the real number and wrote it in the form of a+bi, where A is called the real part of the imaginary number, B is called the imaginary part of the imaginary number, and A and B are both real numbers. When the complex number is a complex number,
That is known: when b=0 and z=a, then the complex number becomes a real number; When a=0, b≠0 and z=bi, we call it pure imaginary number.
Necessary and sufficient conditions for negative numbers to be pure imaginary numbers;
1: z = a+bi (a, b ∈ r) is a pure imaginary number.
2:z is a pure imaginary number.
3: z is a pure imaginary number.