Two complex numbers in polar form #z_1=r_1(cosalpha+isinalpha)# and #z_2=r_2(cosbeta+isinbeta)# can be multiplied as under,
#z_1*z_2=r_1*r_2[cosalphacosbeta+icosalphasinbeta+isinalphacosbeta+i^2sinalphasinbeta]#
= #r_1*r_2[(cosalphacosbeta-sinalphasinbeta)+i(cosalphasinbeta+sinalphacosbeta)]#
= #r_1*r_2[cos(alpha+beta)+isin(alpha+beta)]#
Hence #(0.45(cos310^@+isin310^@))(0.6(cos200^@+isin200^@))#
= #0.45xx0.6(cos(310^@+200^@)+isin(310^@+200^@))#
= #0.27(cos510^@+isin510^@)#
= #0.27(cos(360^@+150^@)+isin(360^@+150^@))#
= #0.27(cos150^@+isin150^@)#
= #0.27(-sqrt3/2+1/2i)#
