Answer:
Attachment 1 : Option C
Attachment 2 : Option A
Step-by-step explanation:
( 1 ) Expressing the product of z1 and z2 would be as follows,
Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,
cos(π / 5) = ,
sin(π / 5) =
cos(3π / 2) = 0,
sin(3π / 2) = - 1
Let's substitute those values in our expression,
And now simplify the expression,
The exact value of =
and
=
Therefore we have the expression
, which is close to option c. As you can see they approximated the solution.
( 2 ) Here we will apply the following trivial identities,
cos(π / 3) = ,
sin(π / 3) = ,
cos(- π / 6) = ,
sin(- π / 6) =
Substitute into the following expression, representing the quotient of the given values of z1 and z2,
⇒
The simplified expression will be the following,
or in other words
or
The solution will be option a, as you can see.