Question

How do you simplify `1/2(cos(pi/3)+isin(pi/3))div 3(cos(pi/6)+ising(pi/6))` and express the result in rectangular form?

Answer 1

`1/6 i`

Explanation:

Using Euler's formula,

`cos theta +i sin theta = e^(i theta)`, the given problem reduces to,
`(1/2 e^(i pi/3)) / (3 e^(i pi/6)`

`1/6 e^i( pi/3 -pi/6)`

`1/6 e^(i pi/2)`

`1/6 (cos (pi/2) +i sin (pi/2))`

`1/6 i`....................... [ `cos (pi/2) =0 and sin (pi/2) =1`]