Posted by batmo on .
Given Z = 2(cos 148° + isin 148°) and W = 5(cos 11° + isin 11°), find and simplify z/w.
10(cos 137° – isin 137°)
0.4(cos 137° + isin 137°)
0.4(cos 137° – isin 137°)
10(cos 137° + isin 137°)

Calculus 
Reiny,
multiply top and bottom by the conjugate of the denominator, that is, multiply top and bottom by
(cos11  isin11)
(I will skip the ° sign)
expand and simplify to get
(2/5) (cos148cos11  icos148sin11 + isin148cos11  i^2sin148sin11)/(cos^2 11  i^2 cos^2 11)
= (2/5) (cos148cos11  cos148sin11 + i(sin148cos11  cos148sin11)/ 1
= .4( cos(14811) + i(sin(14811))
= .4(cos 137 + sin137)
which is one of the choices.