Please help asap. Thanks.

What is the modulus and argument after (StartRoot 3 EndRoot) (cosine (StartFraction pi Over 18 EndFraction) + I sine (StartFract

fgiga [73]

Answer:

$|z| = 27$ -- Modulus

$\theta = \frac{\pi}{3}$ --- Argument

Step-by-step explanation:

Given

$((\sqrt 3)(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18}))^6$

Required

Determine the modulus and the argument

We have that:

$z = ((\sqrt 3)(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18}))^6$

Expand:

$z = (\sqrt 3)^6(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6$

$z = 27(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6$

A complex equation can be expressed as:

$z = |z| e^{i\theta}$

Where

$|z| = modulus$

$\theta = argument$

Where

$e^{i\theta} = (cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})$

So:

$z = 27(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6$ becomes

$z = 27(e^{i\frac{\pi}{18}})^6$

By comparison:

$e^{i\theta} = (e^{i\frac{\pi}{18}})^6$

This gives:

${i\theta} = i\frac{\pi}{18}}*6$

${i\theta} = i\frac{6\pi}{18}}$

${i\theta} = i\frac{\pi}{3}}$

Divide through by i

$\theta = \frac{\pi}{3}$

Hence, the modulus, z is:

$|z| = 27$

And the argument $\theta$ is

$\theta = \frac{\pi}{3}$

4 0

3 years ago

Using technology, determine the monthly payment on a 35 month loan of $28,000 at 8.1% compounded monthly. Round your answer to t

miv72 [106K]

Answer: a

Step-by-step explanation:

Took test

8 0

3 years ago

A store charges $13.75 for 5 boxes of cookies. A second store charges $9.00 for 4 boxes of cookies, but you have to buy a gal

belka [17]

Answer: The number of boxes of cookies that makes the costs equal is 3

Step-by-step explanation:

A store charges $13.75 for 5 boxes of cookies. This means the charge per cookie is 13.75/5 = $2.75

Therefore, for x cookies, the store charges 2.75 × x = $2.75x

A second store charges $9.00 for 4 boxes of cookies. This means the charge per cookie is 9/4 = $2.25

Therefore, for x cookies, the store charges 2.25 × x = $2.25x but you have to buy a gallon of milk for $1.50 to get that deal.

This means that at the second store, the charge for x cookies will be

2.25x + 1.50. Therefore, the cost model equations for both boxes are

Cost of x boxes cookies at first store, C(x)= $2.75x

Cost of x boxes of cookies at second store, C(x) = 2.25x + 1.50

To find number of boxes of cookies that make both costs equal,

2.75x = 2.25x + 1.50

2.75x - 2.25x = 1.50

0.5x = 1.5

x = 1.5/0.5 = 3

5 0

3 years ago

Select the correct answer from each drop-down menu.

natka813 [3]

Answer: (1,0), increases, x=0, decreases to negative infinity.

Step-by-step explanation:

Plato/edmentum

8 0

3 years ago

R + s² at r = 4, s = 1 ( Pls show work) AND NO LINKS THX UwU

icang [17]

r+s^2

4+1^2

4+2

6

Hopefully this helped

Cani get the brainliest please

5 0

3 years ago