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3 years ago

PLEASE HELP ME! I WILL MARK AS BRAINLIEST!!

Mathematics

1 answer:

Natalija [7]3 years ago

5 0

I can't see the problem

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Find the complex fourth roots \[-\sqrt{3}+\iota \] in polar form.

____ [38]

Let $z=-\sqrt3+i$ . Then

$|z|=\sqrt{(-\sqrt3)^2+1^2}=2$

$z$ lies in the second quadrant, so

$\arg z=\pi+\tan^{-1}\left(-\dfrac1{\sqrt3}\right)=\dfrac{5\pi}6$

So we have

$z=2e^{i5\pi/6}$

and the fourth roots of $z$ are

$2^{1/4}e^{i(5\pi/6+k\pi)/4}$

where $k\in\{0,1,2,3\}$ . In particular, they are

$2^{1/4}e^{i(5\pi/6)/4}=2^{1/4}e^{i5\pi/24}$

$2^{1/4}e^{i(5\pi/6+2\pi)/4}=2^{1/4}e^{i17\pi/24}$

$2^{1/4}e^{i(5\pi/6+4\pi)/4}=2^{1/4}e^{i29\pi/24}$

$2^{1/4}e^{i(5\pi/6+6\pi)/4}=2^{1/4}e^{i41\pi/24}$

7 0

2 years ago

n airplane took off from an airport and traveled at a constant rate and angle of elevation. When the airplane reached an altitud

hram777 [196]

The angle of the plane when it rose from the ground is 64.8 degrees

<h3>Application of trigonometry identity</h3>

Given the following parameters from the question

Altitude of the airplane H = 500m

Horizontal distance from airport "d" = 235

Required

angle of elevation

According to the trigonometry identity

tan x = opposite/adjacent

tan x = H/d
tan x = 500/235

tan x = 2.1277

x = arctan(2.1277)

x = 64.8 degrees

The angle of the plane when it rose from the ground is 64.8 degrees

Learn more on angle of elevation here: brainly.com/question/88158

#SPJ1

7 0

1 year ago

A company makes two models of television.

VLD [36.1K]

Answer:

16/25

Step-by-step explanation:

length of screen B=44*(5/4)=55cm

and its width=32*(5/4)=40cm

so, screen B had dimensions 55cm by 40 cm

screen A area=44*32 cm sqr

screen B area=55*40 cm sqr

so, model A screen area/model B screen area

=(44*32)/(55*40)

=16/25

5 0

3 years ago

What are the coordinates of the point (1, –6) after a counter clockwise rotation of 90° about the origin?

IgorLugansk [536]

(-6 ,-1) is the correct answer

4 0

2 years ago

Read 2 more answers

Eighty-eight less than m is smaller than -176.<br> Answer in interval notation

IrinaK [193]

Answer:

(- ∞ , 88)

Step-by-step explanation:

1) m - 88 < - 176

add 88 to both sides

2) m < -88

3) interval notation: ( - ∞, 88)

8 0

3 years ago