Simplify, Show work
1: 2i^20 + i^42
2: i^101 - i^2

Answers

Answer 1

Answer:

1. i^20 X (2+i^22)

2. i² X (i¹¹-1) X (i²² + i¹¹ + 1) X (i^66 + i³³ + 1)

Step-by-step explanation:

1) 2i^20 + i^42

factor out i^20

i^20 X (2 + i^22)

2) i^101 - i²

i²X(i^99-1)

i²X(i³³-1)X(i^66+i³³+1)

Using a³-b³=(a-b)(a²+ab+b²)

i²X(i¹¹-1)X(i²²+i¹¹+1)X(i^66+i³³+1)

i²X(i¹¹-1)X(i²²+i¹¹+1)X(i^66+i³³+1)

I almost gave up typing. Quite stressful, but its fine


Related Questions

Which of the following is a solution of x^2+6x=-18

Answers

We are provided with a quadratic equation , and we have to find it's roots , but let's recall some things

The Standard Form of a quadratic equation is ax² + bx + c = 0

If D > 0 , then the equation have two real and distinct roots/zeroes .

If D = 0 , then the equation have two equal roots/zeroes .

If D < 0 , then the equation have two imaginary roots/zeroes or you can say that no real roots

Where , D is the Discriminant whose value is b²- 4ac and the roots of the equation are given by a very famous formula called The Quadratic Formula , which is as follows ;

[tex]{\quad {\boxed{\pmb{\bf x = \dfrac{-b \pm \sqrt{D}}{2a}}}}}[/tex]

Now , coming back on the question ;

We are provided with the equation x² + 6x = -18 , so on comparing this equation with the standard form of quadratic equation , we have , a = 1 , b = 6 and c = 18 . Now calculating the Discriminant ;

[tex]{: \implies \quad \sf D=(6)^{2}-4\times 1 \times 18}[/tex]

[tex]{: \implies \quad \sf D=36-72}[/tex]

[tex]{: \implies \quad \sf D=-18}[/tex]

As , D < 0 , so two imaginary roots exist . Now by quadratic formula ;

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm \sqrt{-36}}{2\times 1}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm \sqrt{\underline{6\times 6}\times -1}}{2}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm 6\sqrt{-1}}{2}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm 6\iota}{2} \quad \{\because \sqrt{-1}=\iota\}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{2(-3\pm 3\iota)}{2}}[/tex]

[tex]{\quad \qquad \boxed{\bf \therefore \: x=-3 \pm 3\iota}}[/tex]

i’ll give brainliest please help!!!

Answers

Answer: The third one.

Step-by-step explanation: The hottest time of the day is around 3 p.m. Heat continues building up after noon, when the sun is highest in the sky, as long as more heat is arriving at the earth than leaving.

Answer: All of them

Step-by-step explanation: I think zll of them

circus has 20 performers, of which 6 are dancers.

What is the probability that a randomly selected performer will be a dancer?

Write your answer as a fraction or whole number.

Answers

Answer: 1/4

Step-by-step explanation:

HELP ME ASAP

In the following diagram overline DE || overline FG and overline KL perp FG. What is the measure of angle x?

Angle x = _____°​

Answers

Given:

DE||FG and KL is perpendicular to FG.

To find:

The measure of angle x.

Solution:

If two lies intersect each other, then vertical opposite angles are equal.

[tex]m\angle ACB=63^\circ [/tex]         (Vertically opposite angles)

[tex]m\angle BAC=x^\circ [/tex]         (Vertically opposite angles)

KL is perpendicular to FG.

[tex]m\angle ABC=90^\circ[/tex]

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.

In triangle ABC,

[tex]m\angle ABC+m\angle BAC+m\angle ACB=180^\circ[/tex]

[tex]90^\circ+x^\circ+63^\circ=180^\circ[/tex]

[tex]x^\circ+153^\circ=180^\circ[/tex]

[tex]x^\circ=180^\circ-153^\circ[/tex]

[tex]x^\circ=27^\circ[/tex]

Therefore, the measure of angle x is 27 degrees.

Which point is a solution to ys 3x – 4?

Answers

Answer:(3,1)

Step-by-step explanation:

Find the value of x

I tried to solve, but ny answer did not make any sense do Im not sure how to ;-; Some help would be lovely :)​

Answers

Answer:

x = 25

Step-by-step explanation:

A quadrilateral is inscribed in a circle, so it is a cyclic Quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

Therefore,

3x + 21y = 180°.....(1)

2x + 26y = 180°.....(2)

From equations (1) & (2)

3x + 21 y = 2x + 26y

3x - 2y = 26y - 21y

x = 5y

y = 1/5 x

Plug y = 1/5 x in equation (1)

3x + 21*1/5x = 180

15x + 21x = 180*5

(Multiplying both sides by 5)

36x = 900

x = 900/36

x = 25

3. Reason quantitatively. A figure has vertices P(-3, 1), Q(9, 1), R(3, —7), and S(-9, -7).
a. What is the most specific name that can be given to PQRS? Explain how you know.
b. Find PQ, QR, RS, and SP.
c. What is the perimeter of quadrilateral PQRS?
d. What is the area of quadrilateral PQRS?

Answers

don’t listen to them

given the following in a right triangle the hypotenuse is 200 cm and one of the legs is 45cm what is the lenght of the other leg

A: 194.9 cm
B: 12.4 cm
C: 155 cm
D: 245 cm

Answers

Step-by-step explanation:

Hence the length of other side is 194.87 I.e.194.9 cm

Which of the following does not have any dimension?
Question 7 options:

A)

Line

B)

Ray

C)

Line segment

D)

Point

Answers

Answer:

D

A point has a dimension of 0.

Hope this helped!

It’s point a line and a line segment and ray have a dimension of 1 :)

A window in the shape of a parallelogram has the dimensions given.

What is the area of this window?




20 ft²

24 ft²

28 ft²

40 ft²


i'll give brainlyist

Answers

Answer:

The answer is c, 28 ft! brainliest pls lol

Answer:

20ft

Step-by-step explanation:

I did the quiz and got it right :> (K12)

a) 10 - 3(2a + 3) + 4(a - 6)
Simplify

Answers

2becaude 10a -3 =7 colonial

Answer:

-2a - 23

Step-by-step explanation:

10 - 3(2a+3) + 4(a-6)

10-6a-9 + 4(a-6)

10-6a-9 + 4a - 24

-23-6a+4a

-23-2a

Therefore, -2a - 23 is the answer

hello pls help besties (o˘◡˘o)

Answers

Hello bestie I cannot help you
21 or 69

Louis Partridge
Draco Malfoy
Blaise Zabini
Etc....

Help needed on this question

Answers

Hope this helps!
I’ve attached a photo

four billion, five hundred and seventy million. write this number in figures​

Answers

Answer:

4,575,000,000

Step-by-step explanation:

Answer:

It's 4,570,000,000.

Step-by-step explanation:

The first guy had a typo right after the 7.

please help me asap!!!!

Answers

I can't see them clearly....

for number 2 the answer is A
number 3 is B

will mark brainliest need help with DBA If you had a cube with a side length of 4, how can your write the calculations in exponential form?

Answers

4^3

you can write it like 4 × 4 × 4

you can also call it "Four to the Third power".


PLEASE HELP ME ASAPPPP

Answers

Answer:

The answer is

90 degrees the first one is I don't know about the rest sorry

Step-by-step explanation:

what is the area of the composite figure ​

Answers

Answer:

132cm

Step-by-step explanation:

A pair of Descartes jeans costs $120. If the tax is 13%, how much does the pair of jeans cost including tax?

Answers

Answer:

$135.60

Step-by-step explanation:

120*13%=15.6

15.60+120.00=$135.60

The answer is 135.60 dollars

a pair of boots were $45 they were on sale for $38.25 what percent were they off

Answers

Answer:

15% off

Step-by-step explanation:

Answer:

17.2% off

Step-by-step explanation:

45/100 = 0.45

0.45 x 38.25 = 17.2%

17x(8-5)x5 plz help me by solving this plz

Answers

Answer:

255

Step-by-step explanation:

so you first do the bracket so 8- 5 = 3

then 17 × 3 =51

and 51× 5 = 255

17 x (8-5) x 5

= 17 x (3) x 5

= 17 x 3 x 5

= 17 x 15

= 255

Anyone knows this one ?

Answers

Answer:

looks like it might be 4 but I'm not a 100% sure

Write an equation of the line with a slope of 3 and a y-intercept of 4

Answers

Answer:

y = 3x+4

Step-by-step explanation:

Hope this helps!

Answer:

y=3x+4

Step-by-step explanation:

y=mx+b

m is the slope

b is the y-intercept

y=3x+4

Write the equation of the line in fully simplified slope-intercept form?​

Answers

Answer:

ok

Step-by-step explanation:

Answer:

y=-1/2x-1

Step-by-step explanation:

what fraction repsents 0.64​

Answers

Answer:

64/100 = 16/25

Answer:

0.64 in fraction

= 64/100 = 16/25

because each decimal equal to one zero

hope it helps

roberto earns $5 per hour plus 65% commision on all his sales. if y represents his sales for one day, which expression represents robertos total earnings for a day when he worked 6 hours?

Answers

edit: 5(6)+.65*y

original was wrong I wasn't thinking


Find the volume of the figure. Round to the
nearest tenth.
1,286.1 units
401.9 units
5,144.6 units
128.6 units

Answers

Answer:

1,286.1 units is the answer

Step-by-step explanation:

your answer may vary depending on what you use for pie, using a calculator with pie on it gave me approx. 1286.79635

volume formula: V=πr^2h

so π*6.4^2*h

π*40.96*10

3.14*409.6

1,286.144

round

1,286.1

URGENT HELPPP !!!!!! Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!

Answers

Answer:

(8,-3)

Step-by-step explanation:

I just added 1 to the x value and added 2 to the y value because that was the difference between point A and the midpoint of the segment.

Hope this helps!

if a = 5, what is the value of a-3?​

Answers

Answer:

2

Step-by-step explanation:

5-3=2

Answer:

2

Step-by-step explanation:

5 - 3 = 2

0.5(12n – 8) = 26
show your work

Answers

Answer:

n=5

Step-by-step explanation:

divide by 0.5

6n-4=26

(add 4 to both sides)

6n=30

Divide both sides by 6

n=5

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