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liubo4ka [24]
3 years ago
10

Find the sum of 9-4i and it’s complex conjugate

Mathematics
1 answer:
weeeeeb [17]3 years ago
4 0

The complex conjugate of something is essentially just taking the opposite sign of the imaginary part. The following are complex conjugates:

a + bi

a - bi

In this case the complex conjugate of 9 - 4i is 9 + 4i

Now we must add them together like so:

(9 - 4i) + (9 + 4i)

9 - 4i + 9 + 4i

^^^Combine like terms

(9 + 9) + (-4i + 4i)

18 + 0

18

As you can see when you add complex conjugates your answer will be a real number

Hope this helped!

~Just a girl in love with Shawn Mendes

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Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y
professor190 [17]

Answer:

Required total charge is 256\pi coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

x^2=y^2\leq 16 so that the charge density at (x,y) is,

\rho (x,y)=2x+2y+2x^2+2y^2

To find total charge on the disk let Q be the total charge and x=r\cos\theta,y=r\sin\theta so that,

Q={\int\int}_Q\rho(x,y) dA                where A is the surface of disk.

=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA

=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta

=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta

=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta

=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta

=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi

=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi

=256\pi

Hence total charge is 256\pi coulombs per square meter.

3 0
3 years ago
In one area, the lowest angle of elevation of the sun in winter is 27.5°. Find the minimum distance x that a plant needing full
Alex73 [517]

Answer:

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Step-by-step explanation:

Here we have the lowest angle of elevation of the sun given as 27.5° and the height of the fence is 5 feet.

We will then find the position to place the plant where the suns rays can get to the base of the plant

Note that the fence is in between the sun and the plant, therefore we have

Height of fence = 5 ft.

Angle of location x from the fence = lowest angle of elevation of the sun, θ

This forms a right angled triangle with the fence as the height and the location of the plant as the base

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