Respuesta :
[tex]\bf \begin{cases}
z_1=12[cos(55^o)+i~sin(55^o)]\\\\
z_2=4[cos(95^o)+i~sin(95^o)]
\end{cases}\\\\
-------------------------------[/tex]
[tex]\bf ~~~~~~\textit{ product of two complex numbers}\\\\ {{ r_1}}[cos({{ \alpha}})+isin({{ \alpha}})]\quad \cdot \quad {{ r_2}}[cos({{ \beta}})+isin({{ \beta}})] \\\\\\ \implies {{ r_1\cdot r_2}}[cos({{ \alpha}} + {{ \beta}})+isin({{ \alpha}} + {{ \beta}})]\\\\ -------------------------------\\\\ z_1\cdot z_2\implies 12\cdot 4[cos(55^o+95^o)+i~sin(55^o+95^o)] \\\\\\ 48[cos(150^o)+i~sin(150^o)] \\\\\\ |~48[cos(150^o)+i~sin(150^o)]~|\implies 48[cos(150^o)+i~sin(150^o)][/tex]
[tex]\bf ~~~~~~\textit{ product of two complex numbers}\\\\ {{ r_1}}[cos({{ \alpha}})+isin({{ \alpha}})]\quad \cdot \quad {{ r_2}}[cos({{ \beta}})+isin({{ \beta}})] \\\\\\ \implies {{ r_1\cdot r_2}}[cos({{ \alpha}} + {{ \beta}})+isin({{ \alpha}} + {{ \beta}})]\\\\ -------------------------------\\\\ z_1\cdot z_2\implies 12\cdot 4[cos(55^o+95^o)+i~sin(55^o+95^o)] \\\\\\ 48[cos(150^o)+i~sin(150^o)] \\\\\\ |~48[cos(150^o)+i~sin(150^o)]~|\implies 48[cos(150^o)+i~sin(150^o)][/tex]
Answer:
The answer is 48
The absolute value of z1 = 12(cos55° + isin55°) times z2 = 4(cos95° + isin95°) gives us 48.
