回答:
#5 / SQRT(29)(COS(0.540)+ ISIN(0.540))~~ 0.79 + 0.48i#
说明:
#( - 3-4i)/(5 + 2I)= - (3 + 4I)/(5 + 2I)#
#Z = A + BI# 可写成 #Z = R(costheta + isintheta)#,哪里
- #R = SQRT(A ^ 2 + B ^ 2)#
- #THETA =黄褐色^ -1(B / A)#
对于 #Z_1 = 3 + 4I#:
#R = SQRT(3 ^ 2 + 4 ^ 2)= 5#
#THETA =黄褐色^ -1(4/3)= ~~ 0927#
对于 #Z_2 = 5 + 2I#:
#R = SQRT(5 ^ 2 + 2 ^ 2)= sqrt29#
#THETA =黄褐色^ -1(2/5)= 0.381 ~~#
对于 #Z_1 / Z_2#:
#Z_1 / Z_2 = R_1 / R_2(COS(theta_1-theta_2)+ ISIN(theta_1-theta_2))#
#Z_1 / Z_2 = 5 / SQRT(29)(COS(0.921-0.381)+ ISIN(0.921-0.381))#
#Z_1 / Z_2 = 5 / SQRT(29)(COS(0.540)+ ISIN(0.540))= 0.79 + 0.48i#
证明:
# - (3 + 4I)/(5 + 2I)*(5-2i)/(5-2i)= - (15 + 20 1-6I + 8)/(25 + 4)=(23 + 14 1)/ 29 = 0.79 + 0.48i#