\({z_1}{z_2} = {r_1}{r_2}\left[ {\cos \left( {{\varphi _1}{\varphi _2}} \right) + i\sin \left( {{\varphi _1}{\varphi _2}} \right)} \right]\)

\({z_1}{z_2} = {r_1}{r_2}\left[ {\cos \left( {{\varphi _1} + {\varphi _2}} \right) + i\sin \left( {{\varphi _1} + {\varphi _2}} \right)} \right]\)

\({z_1}{z_2} = {r_1}{r_2}\left[ {\sin \left( {{\varphi _1}{\varphi _2}} \right) + i\cos \left( {{\varphi _1}{\varphi _2}} \right)} \right]\)

\({z_1}{z_2} = {r_1}{r_2}\left[ {\sin \left( {{\varphi _1} + {\varphi _2}} \right) + i\cos \left( {{\varphi _1} + {\varphi _2}} \right)} \right]\)