回答:
#0.134-0.015i#
说明:
对于一个复杂的数字 #Z = A + BI# 它可以表示为 #Z = R(costheta + isintheta)# 哪里 #R = SQRT(A ^ 2 + B ^ 2)# 和 #THETA =黄褐色^ -1(B / A)#
#(2 + I)/(14 + 9I)=(SQRT(2 ^ 2 + 1 ^ 2)(COS(TAN ^ -1(1/2))+ ISIN(黄褐色^ -1(1/2)) ))/(SQRT(14 ^ 2 + 9 ^ 2)(COS(TAN ^ -1(9/14))+ ISIN(黄褐色^ -1(9/14))))~~(sqrt5(COS(0.46 )+ ISIN(0.46)))/(sqrt277(COS(0.57)+ ISIN(0.57)))#
特定 #Z_1 = R_1(costheta_1 + isintheta_1)# 和 #Z_2 = R_2(costheta_2 + isintheta_2)#, #Z_1 / Z_2 = R_1 / R_2(COS(theta_1-theta_2)+ ISIN(theta_1-theta_2))#
#Z_1 / Z_2 = sqrt5 / sqrt277(COS(0.46-0.57)+ ISIN(0.46-0.57))= sqrt1385 / 277(COS(-0.11)+ ISIN(-0.11))~~ sqrt1385 / 277(0.99-0.11i )~~ 0.134-0.015i#
证明:
#(2 + I)/(14 + 9I)*(14-9i)/(14-9i)=(28-4i + 9)/(14 ^ 2 + 9 ^ 2)=(37-4i)/ 277 ~~ 0.134-0.014i#