1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fiesta28 [93]
3 years ago
13

Simplify i^41 (please help me)

Mathematics
2 answers:
ira [324]3 years ago
8 0

Answer:

i

Step-by-step explanation:

SOVA2 [1]3 years ago
8 0

Answer:  Choice A) i

====================================================

Explanation:

Let's look at the pattern of powers of i

  • i^0 = 1
  • i^1 = i
  • i^2 = (sqrt(-1))^2 -1
  • i^3 = i*i^2 = i*(-1) = -i
  • i^4 = (i^2)^2 = (-1)^2 = 1

We loop back to 1, and the process starts all over again. The cycle is 4 units long. Ie, the pattern repeats every 4 terms.

What this means is that we can use remainders to quickly figure out something like i^41 without having to use a calculator or tons of paper.

Dividing 41/4 leads to a quotient of 10 and a remainder of 1. We only care about the remainder. The remainder 1 means i^41 = i^1 = i

Note how 41 and 1 lead to the same remainder when we divide by 4.

You might be interested in
F(x) = 3x + 2 and g(x) = x + 5 g[f(x)] =
Tema [17]

Answer:

f (2x+1)=6x−2

3 0
3 years ago
Read 2 more answers
In circle D with m \angle CDE= 76m∠CDE=76 and CD=13CD=13 units find area of sector CDE. Round to the nearest hundredth.
Ksju [112]

Answer:

112.03sq. units

Step-by-step explanation:

The area of a sector = theta/360 * πr²

The area of a sector = 76/360 * 3.14 * 13²

The area of a sector = 76/360 * 530.66

The area of a sector = 40,330.16/360

The area of a sector = 112.03sq. units

This gives the area of the sector

7 0
2 years ago
A biology test is worth 100 points and has 36 questions.
Ad libitum [116K]

Answer:

(a) 7 essays and 29 multiple questions

(b) Your friend is incorrect

Step-by-step explanation:

Represent multiple choice with M and essay with E.

So:

M + E= 36 --- Number of questions

2M + 6E = 100 --- Points

Solving (a): Number of question of each type.

Make E the subject of formula in M + E= 36

E = 36 - M

Substitute 36 - M for E in 2M + 6E = 100

2M + 6(36 - M) = 100

2M + 216 - 6M = 100

Collect Like Terms

2M - 6M = 100 - 216

-4M = - 116

Divide both sides by -4

M = \frac{-116}{-4}

M = 29

Substitute 29 for M in E = 36 - M

E = 36 - 29

E = 7

Solving (b): Can the multiple questions worth 4 points each?

It is not possible.

See explanation.

If multiple question worth 4 points each, then

2M + 6E = 100 would be:

4M + xE = 100

Where x represents the number of points for essay questions.

Substitute 7 for E and 29 for M.

4 * 29 + x * 7 = 100

116 + 7x = 100

Subtract 116 from both sides

116-116 + 7x = 100 -116

7x = 100-116

7x = -16

Make x the subject

x = -\frac{16}{7}

Since the essay question can not have worth negative points.

Then, it is impossible to have the multiple questions worth 4 points

<em>Your friend is incorrect.</em>

6 0
2 years ago
How do you complete a tree map withe the following words estimation,benchmark,hundredth ,place value,round,tenth, thousandth
Mashcka [7]
I think  you can put bench mark place valie round tenth thousnadth
3 0
3 years ago
Johan's water bottle holds 4.2L of water. Johan has drank 51% of water in the bottle. How much, in litres, has he drunk?
swat32

Answer : 2.142L

Step-by-step explanation:

51/100 × 4.2

=51/100 × 42/10

= 2142/1000

= 2.142L

8 0
2 years ago
Read 2 more answers
Other questions:
  • *If A invests 40% of his money and B invests 45% of his money, the total investment will be $215,000. If A invests 45% of his mo
    12·1 answer
  • Express the improper fraction as a mixed number in simplest form 39/8
    14·2 answers
  • If the length of a rectangular television screen is 20 inches and its height is 15 inches,
    13·1 answer
  • If you eat four medium strawberries you get 48% of your daily recommended amount of vitamin C.what fraction of your daily amount
    8·1 answer
  • Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
    14·2 answers
  • Please help me for my homework
    12·1 answer
  • Determine the domain and range of the function below<br> <img src="https://tex.z-dn.net/?f=y%3D%5Csqrt%7B2x%7D-4" id="TexFormula
    13·1 answer
  • HELP ASAP!!! (WILL MARK BRAINLIEST)
    10·1 answer
  • Find the reference angle for a rotation of 347º.
    10·1 answer
  • What is the value of 2(-8) (- 5) + 12
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!