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
Taya2010 [7]
3 years ago
12

Which simplifications of the powers of i are correct? There may be more than one correct answer.

Mathematics
1 answer:
fredd [130]3 years ago
6 0

\bf i^2=-1\qquad\qquad i^3=-i\qquad \qquad i^4=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ i^{22}\implies i^{(4\cdot 5)+2}\implies i^{4\cdot 5}i^2\implies (i^4)^5 i^2\implies 1^5(-1)\implies -1~\dotfill \bigotimes \\\\\\ i^{11}\implies i^{(2\cdot 5)+1}\implies (i^2)^5 i\implies (-1)^5(i)\implies -i~\dotfill \checkmark

\bf i^{21}\implies i^{(4\cdot 5)+1}\implies (i^4)^5 i\implies 1^5(i)\implies i~\dotfill \checkmark \\\\\\ i^{12}\implies i^{3\cdot 4}\implies i^3 i^4\implies (-i)(1)\implies -i\dotfill \bigotimes \\\\\\ i^{20}\implies i^{4\cdot 5}\implies (i^4)^5\implies 1~\dotfill \checkmark \\\\\\ i^{26}\implies i^{(4\cdot 6)+2}\implies (i^4)^6 i^2\implies 1^6(-1)\implies -1\dotfill \checkmark \\\\\\ i^{27}\implies i^{(4\cdot 6)+3}\implies (i^4)^6 i^3 \implies 1^6(-i)\implies -i\dotfill \bigotimes

You might be interested in
22.11 divided by 11?
Dimas [21]

Answer: 2.01

Explanation: I rounded 22.11 two 22. So when you divide it by eleven is 2. Then you divide 11 by 11. Which is one, and it seems it was in the hundreths place so you add a cero before the one.


5 0
3 years ago
Find the distance between the point (2, 3) and the line 4x + 3y = 10 (round your answer to the nearest tenth).
Monica [59]

Explanation

Let's first graph the elements:

Using the distance formula we get:

d=\frac{|4(2)+3(3)-10|}{\sqrt{4^2+3^2}}d=\frac{|7|}{\sqrt{25}}=\frac{7}{5}=1.4

4 0
1 year ago
Find the range, median, and mode of the following dot plot.
Aloiza [94]

Answer:

Range: 0.07

Median: 0.145

Mode: none

Step-by-step explanation:

<u>Range:</u> largest #- smallest #

<u>Median:</u> middle number (when numbers are in order least to greatest) or when two are middle number you add them, and divide by two

<u>Mode:</u> most occurring number(s) (if there aren't any, no mode)—but if there are multiples such as 2 zeros and 2 ones then 0 and 1 would be the mode

5 0
3 years ago
2% of the ducks in a pond have a fluffy tail. If 4 ducks have a fluffy tail, how many ducks are in the pond. Please answer best
GuDViN [60]

Answer:

200 ducks total in the pond

Step-by-step explanation:

2% of x equals 4

0.02x = 4

x = 200

6 0
3 years ago
Why did my popularity suddenly jump from 3000 percent to -100
SVETLANKA909090 [29]

Answer:

don't know

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Lily is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pa
    15·1 answer
  • If you answer right ill give you brainly
    15·2 answers
  • The area of a trapezoid is 864cm2. It has a height of 24 cm, and the length of one of its bases is 30 cm. What is the length of
    7·1 answer
  • Identify whether this is a polynomial is a quadratic, linear or neither<br> F (x) =x2 + 3x +4
    6·1 answer
  • What is it called when the variable dosnt have an answer?
    14·2 answers
  • A surveyer wants to know the area of a region that is 212 miles by 314 miles. He uses the given model for help. Which expression
    11·1 answer
  • Simplify the following expression:<br> –10x – 9x + 1
    6·2 answers
  • How do you do this question?
    11·1 answer
  • charles is 22 years older than his sister danielle. in 10 years he will be twice as old as danielle. how old is each of them now
    12·1 answer
  • Fifteen cards numbered 1-15 are placed in a hat. What is the probability that the card has a multiple of 3 on it, given that the
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!