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
satela [25.4K]
3 years ago
6

What is the value of i^97 - i

Mathematics
1 answer:
Vesna [10]3 years ago
8 0

Answer:

0

Step-by-step explanation:

i^1 = i

i^2 = - 1

i^3 = i^2 * i = - 1

i^4 = i^2 * i^2 = -1 * -1 = 1

Now the circle just repeats itself. So what you do is find out the remainder of i^97 which you divide by 4. What you get is 24 with a remainder of 1.

So i^97 = i

i - i = 0

The answer is 0

You might be interested in
ALGEBRA QUESTION PLS HELPS
cluponka [151]

The value of x is –7.

Solution:

Given expression:

$\left(\frac{1}{x+3}+\frac{6}{x^{2}+4 x+3}\right) \cdot \frac{x+3}{x+1}

Let us factor x^2+4x+3.

x^2+4x+3=(x+1)(x+3)

Substitute this in the fraction.

$\left(\frac{1}{x+3}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

To make the denominator same, multiply and divide the first term by (x +1).

$\left(\frac{(x+1)}{(x+1)(x+3)}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

Denominators are same, you can add the fractions.

$\left(\frac{x+1+6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

$\frac{x+7}{(x+1)(x+3)} \cdot \frac{x+3}{x+1}

Cancel the common term in the numerator and denominator.

$\frac{x+7}{x+1} \cdot \frac{1}{x+1}

Multiply the fractions.

$\frac{x+7}{(x+1)^2}

$\frac{x+7}{x^2+2x+1}

The expression is simplified to one rational expression.

Suppose the expression is equal to 0.

$\frac{x+7}{x^2+2x+1}=0

Do cross multiplication.

${x+7}=0\times (}{x^2+2x+1})

Any number or variable multiplied by 0 gives 0.

${x+7}=0

Subtract 7 from both sides of the equation.

${x+7-7}=0-7

x = –7

The value of x is –7.

7 0
3 years ago
Keith receives $25000 salary for working as a account. If keith spends 40% of his salary on expenses each year, then how much mo
Scrat [10]

Answer:

$25000 * 40% = 100.000

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Change these times to 24-hour clock.<br> A- 4:25pm<br> B-3:45 am
ivanzaharov [21]
Are you even in middle school or high school?lol
7 0
3 years ago
Read 2 more answers
Sin A 4/5.<br><br> Find<br> COSA + tan A
Ivahew [28]

Answer:

Step-by-step explanation:

The opposite side (the one not connected to A) = 4

The hypotenuse is 5

The adjacent side needs to be found for the cosine and the tangent.

a^2 + b^2 = c^2

a = opposite side = 4

b = adjacent side = ?

c = hypotenuse = 5

4^2 + x^2 = 5^2

16 + x^2 = 25          

x^2 = 25 - 16

x^2 = 9

x = sqrt(9)

x = 3

cos(A) = adjacent / hypotenuse = 3/5

Tan(A) = opposite / adjacent = 4/3

cos(A) + tan(A) = 3/5 + 4/3

cos(A) + tan(A) = 9/15 + 20/15 = 29/15

4 0
3 years ago
Read 2 more answers
Rotational symmetry is the quality a design has if it maintains all characteristics when it is rotated about an axis lying in it
mrs_skeptik [129]
Answer – TrueA design is said to have Rotational symmetry if all its characteristics remain the same after it has been rotated about an axis lying in its plane. In other words, rotational symmetry is the quality possessed by a shape has when it looks the same after it has undergone some rotation by a partial turn about an axis lying in its plane. Rotational symmetry is also referred to as radial symmetry.

5 0
3 years ago
Read 2 more answers
Other questions:
  • Factor x^2 - 8x + 16
    12·1 answer
  • Tess earned $52 for 4 hours of shoveling snow and $71.50 for 5.5 hours of shoveling snow. How long would she have to shovel snow
    8·2 answers
  • Need help!!! IF YOU KNOW HOW TO DO THIS GO AHEAD AND DO IT BUT IF YOU DONT THEN DONT BOTHER THANKS
    8·2 answers
  • P=2a+2b; P=56, a=12 solve for b
    13·1 answer
  • The vertex from a quadratic function is f(x)=a(x-h)^2+k what is the vertex if each function match the function rule with the coo
    13·2 answers
  • Plzzzzz help me!!!!!
    13·2 answers
  • How much work is done when a girl pushes a lunch cart 15m across the cafeteria with a force of 3N​
    9·1 answer
  • Find the length of side x in simplest radical form with a rational denominator.
    6·1 answer
  • Find the sum of 0.48 and 0.6
    12·1 answer
  • You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!