Because the value of the n power of the complex number I changes periodically, its period 4 is 4. The first power of I is I. The second power of I is-1, the third power of I is -I, and the fourth power of I is 1, so there are: the 4n power of I is equal to 1, the 4n+ 1 power of I is equal to I, and the 4n+2 power of I is equal to-.
Complex number introduction
We call a number in the form of A+Bi (A and B are both real numbers) a complex number, where A is called the real part, B is called the imaginary part, and I is called the imaginary part. When the imaginary part is equal to zero, this complex number can be regarded as a real number; When the imaginary part of z is not equal to zero and the real part is equal to zero, z is often called pure imaginary number.
Complex number field is an algebraic closure of real number field, that is, any polynomial with complex coefficients always has roots in complex number field. Complex number was first put forward by Cardan, a scholar in Milan, Italy, in the16th century. Through the work of D'Alembert, De Moivre, Euler and Gauss, this concept was gradually accepted by mathematicians.