I is one of the complex numbers, expressed as √- 1, also called imaginary unit. Imaginary number refers to an equation that cannot be solved in the real number range, such as x2+ 1=0. So I should be introduced to represent the solution of the equation, which is pure imaginary number.

Pure imaginary number has an important application in the field of mathematics, which is common in natural science fields such as circuits and waves. Through the study of pure imaginary numbers, we can understand natural phenomena more deeply.

I is not a conventional number, and its introduction has changed the rules of mathematical operation. For example, i2=- 1, i3=-i, i? = 1, so the power operation of I is cyclic and is the core of complex number operation.

Complex numbers can be written in the form of a+bi, where a is the real part and b is the imaginary part. In complex number operations, addition and subtraction are similar to those of real numbers, but i2 needs to be replaced by-1 in multiplication to get the correct result.

Euler formula is an important formula in complex number operation, which relates to natural constant E, imaginary unit I and trigonometric identities cos x and sin X. The formula is e (IX) = cosx+isinx.

Euler formula is widely used in engineering, physics and other fields, and can be used to analyze fluctuations, signals and other issues. In addition, Euler formula is also an important product of mathematical aesthetics, which gives us a deeper understanding of the essence of complex number operation.