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3 years ago

I NEED HELP FAST PLS HELP

Mathematics

1 answer:

netineya [11]3 years ago

7 0

Answer: c

they can all be multipled by 5

Step-by-step explanation:

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Precal help if you could could you answer both. Me finishing this helps me graduate.

oee [108]

Exercise 1:

The easiest way to compute powers of complex numbers is to write them in the form

$z = \rho e^{i\theta} = \rho(\cos(\theta)+i\sin(\theta))$

In this form, you have

$z^n = \rho^n e^{in\theta} = \rho^n(\cos(n\theta)+i\sin(n\theta))$

The magnitude of the number is given by

$z=a+bi \implies \rho = \sqrt{a^2+b^2}$

So, we have

$z=-1+\sqrt{3}i \implies \rho = \sqrt{1+3}=2$

As for the angle, we have

$z=a+bi \implies \theta = \text{atan2}\dfrac{b}{a}$

So, we have

$z=-1+\sqrt{3}i \implies \theta = \text{atan2}\left(\dfrac{-\sqrt{3}}{-1}\right) = -\dfrac{2\pi}{3}$

Finally,

$z=-1-\sqrt{3}i = 2\left(\cos\left( -\dfrac{2\pi}{3}\right) + i\sin\left( -\dfrac{2\pi}{3}\right)\right) \implies z^6 = 2^6\left(\cos\left( -4\pi\right) + i\sin\left(-4\pi\right)\right) = 64$

Exercise 2:

You simply have to compute the trigonometric function:

$\cos\left(-\dfrac{\pi}{4}\right) = \dfrac{\sqrt{2}}{2},\quad \sin\left(-\dfrac{\pi}{4}\right) = -\dfrac{\sqrt{2}}{2}$

So, we have

$z = \sqrt{2}\left(\dfrac{\sqrt{2}}{2} - i\dfrac{\sqrt{2}}{2}\right) = 1-i$

7 0

3 years ago

Find the midpoint of A and B where A has coordinates (-7, 1)<br> and B has coordinates (3,-5).

zepelin [54]

Answer:

A (-7, 1) = (X1, Y1)

B (3, -5) = (X1, Y2)

Now,

Mid point = (X1 + X2÷2, Y1 + Y2 ÷ 2)

= {-7+3÷2, 1+(-5)÷2}

= (-4÷2, 1-5÷2)

= (-4÷2, -4÷2)

= (-2, -2)

Step-by-step explanation:

I hope it will help you to study.

3 0

2 years ago

Given the data set (200,150,325,100,75) find the mean of the data set

Nina [5.8K]

To find the mean (average), u add up all the numbers, then divide by how many numbers there are.

(200 + 150 + 325 + 100 + 75) / 5 = 850/5 = 170 <== the mean

7 0

3 years ago

What is 2 3/4 - 5/16

Ilya [14]

Answer:

2 7/16

Step-by-step explanation:

multiply both top and bottom of 2 3/4 to make it 12/16 then subtract from there.

6 0

3 years ago

Read 2 more answers

2/15 voted omar, 3/5 voted scott, how many voted for Lindsay?

Talja [164]

2/15 and 3/5 share 15 as the least common denominator, hence, added up, it equals 11/15. Lindsay has 4/15 votes.

7 0

2 years ago