we have the expression
[tex]12\sqrt{2}cis(\frac{7pi}{6})\colon3\sqrt{3}cis(\frac{pi}{4})[/tex]
therefore
[tex]12\sqrt{2}c\imaginaryI s(\frac{7p\imaginaryI}{6})\operatorname{\colon}3\sqrt{3}c\imaginaryI s(\frac{p\imaginaryI}{4})=\frac{12\sqrt{2}}{3\sqrt{3}}cis(\frac{7pi}{6}-\frac{pi}{4})=4\sqrt{\frac{2}{3}}cis(\frac{11pi}{12})[/tex]
Simplify
[tex]4\frac{\sqrt{6}}{3}cis(\frac{11pi}{12})[/tex]
