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2 years ago

Why does the expression i to the power 4n+2 is always equal to -1

Mathematics

1 answer:

Alexandra [31]2 years ago

7 0

Answer:

See Below.

Step-by-step explanation:

We are given:

$i^{4n+2}$

Using exponent properties:

$=i^{4n}\cdot i^2$

Rewriting:

$=(i^4)^n\cdot i^2$

Since i⁴ = 1 and i² = -1:

$=(1)^n\cdot -1$

1 to any power is still 1:

$=1\cdot -1 = -1$

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ddd [48]

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2 years ago

1)a customer buys 2 shirts and pair athletic shoes. The shirts are priced the same. The customer spends a total of $95 .Write an

gulaghasi [49]

Answer 1:

For problem 1, each shirt can cost $15. Since their are two shirts, the price would equal up to $30. The remaining money can be the price of the athletic shoes, which is $65.

Equation: 15+15+65=95

Answer 2:

For problem 2, the pair of dress slacks can cost $55, the dress shoes can cost $100, and the and the blazer can cost $145.

Equation: 55+100+145=300

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3 years ago

The cost of 2 baseball bats, one aluminum, one wooden, is $300. If the aluminum bat costs $40 more than the wooden bat, how much

svp [43]

A + w = 300
a = w + 40

(w + 40) + w = 300
2w + 40 = 300
2w = 300 - 40
2w = 260
w = 260/2
w = 130 <=== cost of wooden bat

a = w + 40
a = 130 + 40
a = 170 <=== cost of aluminum bat

8 0

3 years ago

Read 2 more answers

1) Mr. Rios bought a house in 1960 for $20,000. The value of the house increased by

lana [24]

Answer:

A = 20,000(1.05)^x

Step-by-step explanation:

To get the approximate value of the house after x years, we will use the compound interest formula

A = P(1+r)^n

P is the principal = $20,000 (cost of house)

r is the rate = 5% = 0.05

x is the time

Substitute into the expressio

A = 20,000(1+0.05)^x

A = 20,000(1.05)^x

Hence the required expression is A = 20,000(1.05)^x

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3 years ago

Zhang is constructing a loading ramp (BA) that is 4-feet high (AC). The back of the base (BC) must be 12.8 ft. How long must the

inna [77]

The front of the base is 1.25 ft and the total base is 14.05 ft.

<h3>How to find the side of a right triangle?</h3>

A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

The sides CD and BD can be found using similar triangle principle.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, the following proportion can be established as follows;

$\frac{BC}{AC}=\frac{AC}{CD}$

Hence,

$\frac{12.8}{4}=\frac{4}{CD}$

cross multiply

4 × 4 = 12.8 CD

16 = 12.8CD

divide both sides by 12.8

CD = 16 / 12.8

CD = 1.25 ft

BD = 1.25 + 12.8 = 14.05 ft

Therefore, the front of the base is 1.25 ft and the total base is 14.05 ft.

learn more on right triangle here: brainly.com/question/14324872

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2 years ago

Why does the expression i to the power 4n+2 is always equal to -1​

Why does the expression i to the power 4n+2 is always equal to -1