All categories

2 years ago

Complete the following exercises by applying polynomial identities to complex numbers.

Mathematics

1 answer:

erik [133]2 years ago

6 0

1.)

=(x-8i)(x+8i)

x^2+8ix-8ix-64i^2

x^2-64i^2

x^2-64(-1)

x^2+64

2.)

=(4x-7i)(4x+7i)

16x^2+28ix-28ix-49i^2

16x^2-49i^2

16x^2-49(-1)

16x^2+49

3.)

=(x+9i)(x+9i)

x^2+9ix+9ix+81i^2

x^2+18ix+81(-1)

x^2+18ix-81

4.)

=(x-2i)(x-2i)

x^2-2ix-2ix+4i^2

x^2-4ix+4(-1)

x^2-4ix-4

5.)

=[x+(3+5i)]^2

(x+5i+3)^2

(x+5i+3)(x+5i+3)

x^2+5ix+3x+5ix+25i^2+15i+3x+15i+9

x^2+6x+10ix+30i+25i^2+9

x^2+6x+10ix+30i+25(-1)+9

x^2+6x+10ix+30i-25+9

x^2+6x+10ix+30i-16

Hope this helps :)

You might be interested in

If you help me I will love you forever

joja [24]

Answer:

I think the answer would be 22.15 but I'm not really sure.

7 0

2 years ago

Read 2 more answers

Under a translation of 5 units up and 2 units to the left, the point (3,4) will become

Vedmedyk [2.9K]

The point would become (8,2)
3+5=8
4-2=2

4 0

3 years ago

(2, 7) and (-6, -2) find the distance between each pair of points

yaroslaw [1]

Answer:

$\sqrt{145}$

Step-by-step explanation:

Hi there!

We are given the points (2, 7) and (-6, -2). We want to find the distance between them. To do that, we can use the distance formula

The distance formula is given as $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are points

We have 2 points, which is what we need to find the distance, but let's label their values to avoid any confusion

$x_1=2\\y_1=7\\x_2=-6\\y_2=-2$

Now substitute those values into the formula:

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\sqrt{(-6-2)^2+(-2-7)^2}$

Simplify the values under the radical:

$\sqrt{(-8)^2+(-9)^2}$

Raise to the second power:

$\sqrt{64+81}$

Add the numbers under the radical together

$\sqrt{145}$

The answer can be left as that, as the radical cannot be simplified.

Hope this helps!

7 0

2 years ago

Which value is included in the solution set for the inequality graphed on the number line?

GenaCL600 [577]

Answer:

Step-by-step explanation:

4 0

2 years ago

(8m-3n)^2 - (4m+3n)^2

natulia [17]

Answer:

$48m^2-72mn$

Step-by-step explanation:

We need to solve $(8m-3n)^2 - (4m+3n)^2$

We know that,

$(a+b)^2=a^2+b^2+2ab\\\\(a-b)^2=a^2+b^2-2ab$

Using the above formula,

$(8m-3n)^2 - (4m+3n)^2=(8m)^2+(3n)^2-2(8m)(3n)-[(4m)^2+(3n)^2+2(4m)(3n)]\\\\=64m^2+9n^2-48mn-(16m^2+9n^2+24mn)\\\\=64m^2+9n^2-48mn-16m^2-9n^2-24mn\\\\=48m^2-48mn-24mn\\\\=48m^2-72mn$

So, the final answer is $48m^2-72mn$ .

4 0

2 years ago