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3 years ago

PLEASE HELP ME!!!!

Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

5 0

Answer:

AB² = VAC²-BC²

= V8²-6²

= V64-36 = V28

AB = V7×4 = 2V7 = 5.29

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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

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

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