All categories

3 years ago

Simplify: 1 + i + i^2 + i^3 +i^4 +i^5 if i^2 =-1.

SAT

2 answers:

Aloiza [94]3 years ago

7 0

Answer: 1 + i

Explanation:

Vika [28.1K]3 years ago

3 0

1 + i + i ² + i ³ + i ⁴ + i ⁵ = 1 + i + i ² (1 + i + i ² + i ³)

… = 1 + i + i ² (1 + i + i ² (1 + i ))

… = 1 + i + (-1) (1 + i + (-1) (1 + i ))

… = 1 + i + (-1) (1 + i - 1 - i )

… = 1 + i

Alternatively, notice that

1 - i ⁶ = (1 - i ) (1 + i + i ² + i ³ + i ⁴ + i ⁵)

so that

1 + i + i ² + i ³ + i ⁴ + i ⁵ = (1 - i ⁶) / (1 - i )

Now, i ⁶ = (i ²)³ = (-1)³ = -1, so

1 + i + i ² + i ³ + i ⁴ + i ⁵ = (1 - (-1)) / (1 - i )

… = 2 / (1 - i )

Multiply the numerator and denominator by the conjugate of 1 - i :

… = 2 (1 + i ) / ((1 - i ) (1 + i ))

… = 2 (1 + i ) / (1² - i ²)

… = 2 (1 + i ) / (1 + 1)

… = 1 + i

You might be interested in

When looking at the night sky, many stars can be seen. What is true about all the stars seen in the night sky?

Vladimir [108]

B c and d. I think these are the answers

3 0

3 years ago

In order to clear out room for new merchandise, james decided to mark down some of the items for sale in his electronics store.

Jobisdone [24]

The dvd player’s price was reduced by $3. 82 more than the stereo tuner’s price.

Let the cost price of dvd players be D.

Let the cost price of stereo tuners be S.

Given the following data:

Markdown for dvd player = 36%

Markdown for stereo tuner = 22%

Markdown cost for dvd player = $41.60

Markdown cost for stereo tuner = $69.42

To determine which item’s price was reduced by more, and by how many dollars:

First of all, we would calculate the cost price of each item.

For dvd players:

Note: You'll pay 64% since it was markdown by 36%.

$\frac{64}{100} \times D = 41.60\\\\64D=41.60 \times 100\\\\64D=4160\\\\D=\frac{4160}{64}$

D = $65

Reduction: Dvd player = $65-41. 60=$ $23.40

For stereo tuners:

Note: You'll pay 78% since it was markdown by 22%.

$\frac{78}{100} \times S = 69.42\\\\78S=69.42 \times 100\\\\78S=6942\\\\S=\frac{6942}{78}$

D = $89

Reduction: Stereo tuner = $89-69. 42=$ $19.58

Now, we can calculate the difference in reduction of the cost price of both items:

$Difference = 23.4 -19.58$

Difference = $3.82

Therefore, the price of the dvd players was reduced by $3. 82 more than the price of the stereo tuners.

Read more on markdown here: brainly.com/question/11676563

7 0

2 years ago

How do you plant strawberry seeds answer at any time

Ipatiy [6.2K]

Answer:

Throw seeds down and water it with salt water

Explanation:

8 0

3 years ago

Read 2 more answers

a solid object heated to 120 celsius is placed in a container of water at 33 celsius. What is the best explanation

Softa [21]

The correct answer is C) The temperature of the water will increase; the temperature of the solid will decrease.

In fact, the solid is at higher temperature, so when it is put inside the water it starts to release heat to the water. As a result, the temperature of the solid decreases, and since the heat is absorbed by the water, the temperature of the water increases. This process continues until the water and the solid reach thermal equilibrium (i.e. until they reach same temperature).

7 0

3 years ago

Display the details for just the office expenses group

Fed [463]

In order to display the details for just the Office Expenses group, you should click on the "+ symbol" next to row.

<h3>What is Microsoft Excel?</h3>

Microsoft Excel is a software application that is designed and developed by Microsoft Inc., for analyzing and displaying spreadsheet documents by using rows and columns in a tabulated format.

<h3>What is a spreadsheet?</h3>

In Computer technology, a spreadsheet can be defined as a document which comprises cells that are arranged in a tabulated format with rows and columns. Also, a spreadsheet is typically used in various field to do the following on a data:

Sort

Calculate

Format

Arrange

In this scenario, you should click on the "+ symbol" next to row in your Microsoft Excel software, in order to display the details for the Office Expenses group only.

Read more on spreadsheets here: brainly.com/question/4965119

#SPJ1

4 0

2 years ago