Can somebody explain how trigonometric form polar equations are divided/multiplied?

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.

x = 12

y = 1

for the points!

the correct answer option is (2x-3)(2x+3).

step-by-step explanation:

we are given the following expression and we are to factorize it:

we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.

the two such factors of 36 are negative six and postive six.

factorizing the given expression to get:

therefore, the correct factorization of is (2x-3)(2x+3).