回答:
#5 /平方(29)(cos(0.540)+ isin(0.540))~~ 0.79 + 0.48i#
説明:
#( - 3-4i)/(5 + 2i)= - (3 + 4i)/(5 + 2i)#
#z = a + bi# と書くことができます #z = r(costheta + isintheta)#どこで
- #r = sqrt(a ^ 2 + b ^ 2)#
- #theta = tan ^ -1(b / a)#
にとって #z_1 = 3 + 4i#:
#r = sqrt(3 ^ 2 + 4 ^ 2)= 5#
#theta = tan ^ -1(4/3)= ~~ 0,927#
にとって #z_2 = 5 + 2i#:
#r = sqrt(5 ^ 2 + 2 ^ 2)= sqrt29#
#theta = tan ^ -1(2/5)= ~~ 0.381#
にとって #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 /平方メートル(29)(cos(0.540)+ isin(0.540))= 0.79 + 0.48i#
証明:
# - (3 + 4i)/(5 + 2i)*(5-2i)/(5-2i)= - (15 + 20i-6i + 8)/(25 + 4)=(23 + 14i)/ 29 = 0.79 + 0.48i#