In mathematics, imaginary numbers are numbers in the form of a+b*i, where a and b are real numbers, b≠0, and 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 horizontal axis and the imaginary part B can correspond to the vertical axis on the plane, so that the imaginary number a+b*i can correspond to the points (a, b) on the plane.

Four operations:

(a+bi) (c+di)=(a c)+(b d)i

(a+bi)(c+di)=(ac-bd)+(ad+bc)i

(a+bi)/(c+di)=(ac+bd)/(c？ +d？ )+(bc-ad)i/(c？ +d？ )

r 1(isina+cosa)R2(isin b+cosb)= r 1r 2[cos(a+b)+isin(a+b)]

r 1(isina+cosa)/R2(isin b+cosb)= r 1/R2[cos(a-b)+isin(a-b)]