$z=2\sqrt{2}\left(\cos\left(\frac{7\pi}{4}\right)+i\sin\left(\frac{7\pi}{4}\right)\right)$

$\left. \begin{array} { l } {\text{Given two complex numbers } z _ { 1 } = r _ { 1 } ( \operatorname { cos } ( a ) + i \operatorname { sin } ( a ) ) \text { and } z _ { 2 } = r _ { 2 } \operatorname {( cos } ( b )+i\text{ sin}(b)) } \\ { \text { The product of the two numbers is } z _ { 1 } z _ { 2 } = r _ { 1 } r _ { 2 } ( \operatorname { cos } ( a + b ) + i \operatorname { sin } ( a + b ) ) } \\ { \text { The quotient of the two numbers is } \frac { z _ { 1 } } { z _ { 2 } } = \frac { r _ { 1 } } { r _ { 2 } } ( \operatorname { cos } ( a - b ) + i \operatorname { sin } ( a - b ) ) } \end{array} \right.$