Final Exam Review 1 - Scf

Products and Quotients in Trigonometric Form & DeMoivre’s Theorem
In questions 39 – 40 find the product 1 2 z z ⋅ and the quotient
z
form.
o
o
o
o
39. z = ( cos25
+ isin
25 ) and z = 3(
cos40
+ isin
40 )
1
5 2
o
o
o
o
40. z = (cos50
+ isin
50 ) and z = 2(cos20
+ isin
20 )
1
10 2
41. Given z = 1+
i 3 and z = − 3 + i
1
a) Find the product 1 2 z z ⋅ in standard form.
2
b) Then, write z 1 and z 2 in trigonometric form.
c) Now, find their product in trigonometric form.
z 1
. Leave your answer in trigonometric
d) Convert the answer that is in trigonometric form to standard form to show that the two
products are equal.
In questions 42– 43 use Demoivre’s Theorem to find each of the following . Write your answer in
standard a + bi form.
[ ] 4
o
o
42. 2(
cos150
+ isin150
)
43. ( ) 4
−
3 + i
2