Question #baaba

Question

257 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-15T20:43:48

see below

if# " "z_1=r_1(costheta_1+isintheta_1)#

#" & " z_2=r_2(costheta_2+isintheta_2)#

#or z_1=r_1e^(itheta_1)#

#z_2=r_2e^(itheta_2)#

#z_1z_2=r_1e^(itheta_1)r_2e^(itheta_2)#

#=r_1r_2e^(i(theta_1+theta_2))#

#=>z_1z_2=r_1r_2(cos(theta_1+theta_2)+isin(theta_1+theta_2))#

so we have

#z_1=12(cos60+isin60)#

#z_2=3(cos45+isin45)#

#:.z_1z_2=(12xx3)(cos(60+45)+isin(60+45))#

#z_1z_2=36(cos105+isin105)#

likewise

#z_1/z_2=r_1/r_2(cos(theta_1-theta_2)+isin(theta_1-theta_2))#

in this case

#z_1/z_2=12/3(cos(60-45)+isin(60-45))#

#z_1/z_2=4(cos15+isin15)#