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2 years ago

What is the value of i 97 – i? –i 0 –2i i Superscript 96

2 answers:

6 0

<em>The question is not clearly readable, but I'm assuming the expression which makes more sense, so you can have a clue</em>

Answer:

$i^{97}-i=0$

Step-by-step explanation:

<u>Powers of The Imaginary Unit</u>

The imaginary unit i is defined as

$i=\sqrt{-1}$

The first powers of i are

$i^0=1$

$i^1=i$

$i^2=(\sqrt{-1})^2=-1$

$i^3=i.i^2=-i$

$i^4=i^2.i^2=1$

And so on the cycle repeats every four numbers. To find the value of $i^{96}$ we can find the remainder of 96/4=0. So $i^{96}=i^0=1$

The given expression is

$i^{97}-i$

Factoring

$i(i^{96}-1)$

Since $i^{96}=1$

$=i(1-1)=0$

The required value is 0

anyanavicka [17]2 years ago

5 0

Answer:

The answer is 0

Step-by-step explanation:

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For the system of equations that follows, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in

Rainbow [258]

Answer:

$\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Step-by-step explanation:

From the question we are told that

System of equations given as

x₁ + 3x₂ + x₃ + x₄ = 3;

2x₁ - 2x₂ + x₃ + 2x₄ = 8;

x₁ - 5x₂ + x₄ = 5

Matrix form

$\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}$ $\begin{Vmatrix}x_1\\x_2\\x_3\\x_4\end{Vmatrix}$

Generally the echelon reduction is mathematically applied as

$\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}$

Add -2 times the 1st row to the 2nd row

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & -8 & -1&0&2\\0&1 & -5 & 1& 5\end{Vmatrix}$

Multiply the 2nd row by -1/8

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&1 & -5 & 1& 5\end{Vmatrix}$

Add -1 times the 2nd row to the 3rd row

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & -41/8 & 1& 21/4\end{Vmatrix}$

Multiply the 3rd row by -8/41

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Add -1/8 times the 3rd row to the 2nd row

Add -1 times the 3rd row to the 1st row

$\begin{Vmatrix}1 & 3 & 0&49/41&165/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Add -3 times the 2nd row to the 1st row

$\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

3 0

2 years ago

What is the solution of 3x+2y=22 , 3x-2y=2

irina [24]

3x+2y=22
3x-2y=2
we add these to equations together
6x=24
x=4
then we plug in x to find y
3*4+2y=22
12+2y=22
2y=10
y=5
solution is (4,5) (x=4 and y=5)

5 0

3 years ago

Read 2 more answers

Write an inequality from (–5) to (–1) inclusive

skad [1K]

Answer:

$-5\leq x\leq -1$

Step-by-step explanation:

This is a compound inequality that basically states that the X value is greater than or equal to -5, but less than or equal to -1. It is inclusive, because it includes both numbers and therefore should have an equal to sign ( $\leq or \geq$ ) instead of just less than or greater than ( < or >).

8 0

3 years ago

Margrets parents have her $40 to spend on new video games. Used games are $8 and new games are $14 what is the system of inequal

Artist 52 [7]

8x + 14y = 40
Or
14x + 8y = 40

7 0

2 years ago

Use the function r=a+5 to find the value of r when a=10

Flauer [41]

Answer: 15=10+5

Step-by-step explanation:

Subtract 55 from both sides.

15-5=a

Simplify 15-5 to 10.

10=a

Switch sides.

a=10

3 0

2 years ago