Step 1:
Write the given information
w1 = 20 (cos (140) + i sin (140))
W2 = 4 (cos (35) + i sin (35))
Step 2:
[tex]\begin{gathered} \frac{w_1}{w_2} \\ =\frac{20(\cos 140\text{ + isin140)}}{4(\cos 35\text{ + isin35)}}\text{ } \\ =\text{ }\frac{5(\cos 140\text{ + isin140)}}{\cos 35\text{ + isin35}} \\ =\text{ }\frac{5(\cos 140\text{ + isin140)}}{\cos 35\text{ + isin35}}\text{ }\times\text{ }\frac{\cos 35\text{ - isin35}}{\cos 35\text{ - isin35}} \\ =\text{ }\frac{5(\cos 140\cos 35\text{ - isin35cos140 + isin140cos35 + sin140sin35)}}{\cos ^235+sin^235} \\ =\text{ }\frac{5(\cos (140-35)\text{ - isin(140-35))}}{1}\text{ } \\ =\text{ 5cos105 - i5sin105} \end{gathered}[/tex]
Final answer
[tex]\begin{gathered} =\text{ 5(}\frac{-\sqrt[]{6}+\sqrt[]{2}}{4}\text{) - i5(}\frac{\sqrt[]{6}\text{ + }\sqrt[]{2}}{4}\text{) } \\ \\ or \\ =\text{ 5cos105 - i5sin105} \end{gathered}[/tex]
