- #1

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If w, z are complex numbers

wz = rs( cos[tex]\alpha[/tex] + isin [tex]\alpha[/tex] ) (cos [tex]\varphi[/tex] + isin [tex]\varphi[/tex])

wz = rs(cos[tex]\alpha[/tex] cos [tex]\varphi[/tex] - sin [tex]\alpha[/tex]sin[tex]\varphi[/tex]) + i(sin [tex]\alpha[/tex]cos[tex]\varphi[/tex] + cos [tex]\alpha[/tex] sin [tex]\varphi[/tex]))

wz = rs(cos ([tex]\alpha[/tex] +[tex]\varphi[/tex]) + i sin([tex]\alpha[/tex] +[tex]\varphi[/tex]))

What sort of trigonometric identity is used here between the 2nd and 3rd lines?