Question

W120 (cos (140') + i sin (140))Wo4 (cos (35) + i sin (35))W1What is.?

Answer 1

Step 1:

Write the given information

w1 = 20 (cos (140) + i sin (140))

W2 = 4 (cos (35) + i sin (35))

Step 2:

`\begin{gathered} (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{ }*\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}`

Final answer

`\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}`