Find the following product, and write the product in rectangular form, using exact values.
[8( cos 45° + i sin 45°)][7( cos 165° + i sin 165°)]
[8( cos 45° + i sin 45°)][7(cos 165° + i sin 165°)] = IN
(Type your answer in the form a + bi.)

Writing each complex number in exponential form makes this very easy. Recall Euler's formula:

Then

(since 45º = π/4 rad)

(since 165º = 11π/12 rad)

The product is

and in Cartesian form this is

2

step-by-step explanation:

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.