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2 years ago

What is the value of i4?

Mathematics

1 answer:

natima [27]2 years ago

8 0

Answer:

Step-by-step explanation:

You want to know the value of i^4.

<h3>Powers of i</h3>

The fourth power of i, √(-1), can be found the same way the value of any fourth power can be found: carry out the multiplication.

i^4 = i·i·i·i = -1·i·i = -i·i = -(-1) = 1

The fourth power of i is 1.

Additional comment

As you can see from the evaluation process, ...

i¹ = i

i² = -1 . . . . . definition of i

i³ = -i

i⁴ = 1

The sequence repeats for higher powers.

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What is the horizontal difference between (4, 8) and (-2, 2)?

Stolb23 [73]

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6 units

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4 0

3 years ago

Find a possible formula for a fourth degree polynomial g that has a double zero at -2, g(4) = 0, g(3) = 0, and g(0) = 12. g(x) =

astraxan [27]

<h2>Answer:</h2>

The possible formula for a fourth degree polynomial g is:

$g(x)=\dfrac{1}{4}(x^4-3x^3-12x^2+20x+48)$

<h2>Step-by-step explanation:</h2>

We know that if a polynomial has zeros as a,b,c and d then the possible polynomial form is given by:

$f(x)=m(x-a)(x-b)(x-c)(x-d)$

Here the polynomial g has a double zero at -2, g(4) = 0, g(3) = 0.

This means that the polynomial g(x) is given by:

$g(x)=m(x-(-2))^2(x-4)(x-3)\\\\i.e.\\\\g(x)=m(x+2)^2(x-4)(x-3)\\\\i.e.\\\\g(x)=m(x^2+2^2+2\times 2\times x)(x(x-3)-4(x-3))\\\\i.e.\\\\g(x)=m(x^2+4+4x)(x^2-3x-4x+12)\\\\i.e.\\\\g(x)=m(x^2+4+4x)(x^2-7x+12)\\\\i.e.\\\\g(x)=m[x^2(x^2-7x+12)+4(x^2-7x+12)+4x(x^2-7x+12)]\\\\i.e.\\\\g(x)=m[x^4-7x^3+12x^2+4x^2-28x+48+4x^3-28x^2+48x]\\\\i.e.\\\\g(x)=m[x^4-7x^3+4x^3+12x^2+4x^2-28x^2-28x+48x+48]\\\\i.e.\\\\g(x)=m[x^4-3x^3-12x^2+20x+48]$

Also,

$g(0)=12$

i.e.

$48m=12\\\\i.e.\\\\m=\dfrac{12}{48}\\\\i.e.\\\\m=\dfrac{1}{4}$

Hence, the polynomial g(x) is given by:

$g(x)=\dfrac{1}{4}(x^4-3x^3-12x^2+20x+48)$

8 0

3 years ago

Given that 3x + y = 0 and 2x - y = 5, find the value of y.

professor190 [17]

Answer:

3x + y = 0

x = -y/3

Now, 

2x - y = 5

2 (-y/3) - y = 5

(-2y - 3y)/3 = 5

-5y/3 =5

y=-3

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4 0

4 years ago