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2 years ago

Geometry PLEASE HELP I’m right? Yes or no?

Mathematics

1 answer:

natali 33 [55]2 years ago

4 0

Answer:

Step-by-step explanation:

-2 + 12 = 10

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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

I need the answer pls help me

Fynjy0 [20]

Answer:

A reflection followed by a translation!!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

3 0

3 years ago

How can I get better in mathematics?

aliya0001 [1]

Answer:

STUDY OR TUTOURStep-by-step explanation:

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2 years ago

I need to find what m

Vadim26 [7]

Answer:

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

On Sunday, there were 22 inches of snow. The weather finally began to warm up and by Monday afternoon there were 19 inches. Then

sattari [20]

Answer:

22-3d=x

Step-by-step explanation:

where d is the days that it melts and the amount of snow x is the snow that is left.

3 0

2 years ago