I need help on pre-calculus Exam Question!!

Let p = 2 ( cos(π / 2) + i sin(π / 2)) and q = 5 ( cos(2π / 3) + i sin(2π / 3)). Write the following in standard ( a + bi ) form:

a) p/q
b) pq

c) Find the product and write the result in a+bi form

[4(cos45° + i sin45°)] [3(cos15° + i sin15°)]





The answers are and gotten from the textbook but I really wanna know how to get them
a) √3/5 - 1/5i
b) -5√3 - 5i
c) 6 + 6√3i


IT would help me A LOT if someone can explain how to even begin these problems or solve them all completely and show me how it was done, or link me to sites that does step by step on these equations
PS; if its a site its probably the most simple questions and these questions are very very hard late in the course questions so I really need some expert help or someone who knows their math please.

modulus(p/q)=modp/modq
………………….=2/5
argument(p/q)=argp – argq
…………………= π / 2 - 2π / 3
…………………=-π / 6
Therefore p/q=2/5(cos(- π / 6)+sin(- π / 6))
…………………..=2/5.√3/2 + 2/5.-1/2i
………………….=√3/5 - 1/5 i

mod(pq)=modp.modq
…………..=2x5
…………..=10
arg(pq)=argp + argq
…………= π / 2 + 2π / 3
…………= 7π / 6
pq=10(cos7π / 6+isin7π / 6)
….=10(-√3/2.-1/2i)
….=-5√3-5i

[4(cos45° + i sin45°)] [3(cos15° + i sin15°)]
As above theory
mod(product)=12
arg(product)=45+15
………………….=60
Therefore product = 12(cos60+isin60)
…………=12(1/2+i√3/2)

Sorry i cant help you with the problem but i found a lot of nice links using bing.com http://www.bing.com/search?q=pre-calculu…

theres even a lot of stuff on youtube.com http://www.youtube.com/results?search_qu…

Use De Moivre's theorem
a/
p/q = (2/5)( cos(π / 2 - 2π / 3) + i sin(π / 2 - 2π / 3)) = ...simplify
b/
pq = 10( cos(π / 2 + 2π / 3) + i sin(π / 2 + 2π / 3)) = ...simplify