Question

If z1 = 12(cos55° + isin55°) and z2 = 4(cos95° + isin95°), then |z1z2|= ???

Answer 1

$\bf \begin{cases} z_1=12[cos(55^o)+i~sin(55^o)]\\\\ z_2=4[cos(95^o)+i~sin(95^o)] \end{cases}\\\\ -------------------------------$

$\bf ~~~~~~\textit{ product of two complex numbers}\\\\ {{ r_1}}[cos({{ \alpha}})+isin({{ \alpha}})]\quad \cdot \quad {{ r_2}}[cos({{ \beta}})+isin({{ \beta}})] \\\\\\ \implies {{ r_1\cdot r_2}}[cos({{ \alpha}} + {{ \beta}})+isin({{ \alpha}} + {{ \beta}})]\\\\ -------------------------------\\\\ z_1\cdot z_2\implies 12\cdot 4[cos(55^o+95^o)+i~sin(55^o+95^o)] \\\\\\ 48[cos(150^o)+i~sin(150^o)] \\\\\\ |~48[cos(150^o)+i~sin(150^o)]~|\implies 48[cos(150^o)+i~sin(150^o)]$