Find the Quotient and Write in Rectangular Form $\frac { \sqrt { 3 } ( \cos 315 + i \sin 315 ) } { \sqrt { 6 } ( \cos 45 + i \sin 45 ) }$

Multiple Choice

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
- $\frac { \sqrt { 3 } ( \cos 315 + i \sin 315 ) } { \sqrt { 6 } ( \cos 45 + i \sin 45 ) }$

A) $- \frac { \sqrt { 2 } } { 2 } i$
B) $\frac { \sqrt { 2 } } { 2 } + \frac { \sqrt { 2 } } { 2 } \mathrm { i }$
C) $- \frac { \sqrt { 2 } } { 2 } - \frac { \sqrt { 2 } } { 2 } \mathrm { i }$
D) $\frac { \sqrt { 2 } } { 2 }$