Question

\[z _{1}=5+5 \iota \]
\[= r \cos \theta+\iota r \sin \theta \]
\[r \cos \theta =5,r \sin \theta=5\]
square and add
r=5
divide \[\tan \theta=1=\tan \frac{ \pi }{ 4 },\theta=\frac{ \pi }{ 4 }\]
\[z _{1}=5\left( \cos \frac{ \pi }{ 4 } +\iota \sin \frac{ \pi }{ 4 } \right)=5 e ^{\iota \frac{ \pi }{ 4 }}\]
\[z _{2}=8\left(\cos \frac{3 \pi }{ 7 } +\iota \sin \frac{3 \pi }{ 7 } \right)=8 e ^{\iota \frac{ 3 \pi }{ 7 }}\]
\[z _{1}*z _{2}=5*8e ^{\iota \left( \frac{ \pi }{ 4 } +\frac{ 3 \pi }{ 7 }\right)}=40 e ^{\iota \frac{ 19 \pi }{ 28 }}\]