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Fudgin [204]
3 years ago
7

If (2p + 1) is a prime number, which one of the following digits could be the value of p?

Mathematics
1 answer:
Doss [256]3 years ago
8 0
Mount Chimborazo's
Mount Chimborazo's peak is the furthest point on Earth from Earth's center. The summit is over 6,800 feet [2,072 meters] farther from Earth's center than Mount Everest's summit. Mauna Kea is the tallest mountain from base to peak at more than 33,500 feet [10,210 meters
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20 points and brainliest <br> I’m in quiz in need it asap <br> Number 4
iren [92.7K]

Answer and step-by-step explanation:

The polar form of a complex number a+ib is the number re^{i\theta} where r = \sqrt{a^2+b^2} is called the modulus and \theta = tan^-^1 (\frac ba) is called the argument. You can switch back and forth between the two forms by either remembering the definitions or by graphing the number on Gauss plane. The advantage of using polar form is that when you multiply, divide or raise complex numbers in polar form you just multiply modules and add arguments.

(a) let's first calculate moduli and arguments

r_1 = \sqrt{(-2\sqrt3)^2+2^2}=\sqrt{12+4} = 4\\ \theta_1 = tan^-^1(\frac{2}{-2\sqrt3}) =-\pi/6\\r_2=\sqrt{1^2+1^2}=\sqrt2\\ \theta_2 = tan^-^1(\frac 11)= \pi/4

now we can write the two numbers as

z_1=4e^{-i\frac \pi6}; z_2=e^{i\frac\pi4}

(b) As noted above, the argument of the product is the sum of the arguments of the two numbers:

Arg(z_1\cdot z_2) = Arg(z_1)+Arg(z_2) = -\frac \pi6 + \frac \pi4 = \frac\pi{12}

(c) Similarly, when raising a complex number to any power, you raise the modulus to that power, and then multiply the argument for that value.

(z_1)^1^2=[4e^{-i\frac \pi6}]^1^2=4^1^2\cdot (e^{-i\frac \pi6})^1^2=2^2^4\cdot e^{-i(12)\frac\pi6}\\=2^2^4 e^{-i\cdot2\pi}=2^2^4

Now, in the last step I've used the fact that e^{i(2k\pi+x)} = e^i^x ; k\in \mathbb Z, or in other words, the complex exponential is periodic with 2\pi as a period, same as sine and cosine. You can further compute that power of two with the help of a calculator, it is around 16 million, or leave it as is.

7 0
2 years ago
Wildlife resort has eight elephant cabs born during the summer and now has 31 total how many elephants were ending was there bef
Kipish [7]

The answer would be 23. 31-8=23

4 0
3 years ago
A movie theater sold 1,246 tickets this weekend. If 314 tickets were sold on Friday and 529 tickets were sold on sunday
Lisa [10]

Answer:

Saturday=403 tickets

Step-by-step explanation:

1246-314-529=403

6 0
3 years ago
Which measurement is the greatest 6kilometers 60meters 600centimeters or 6000 millime
Anna35 [415]
Kilometers are because if you multiply them by 1000 they would be 6000 and meter divide by 100 would be 6 and millimeters divide by 1000 would be 6 so 6000, 60, 6, 6
6 0
3 years ago
Read 2 more answers
The first step when dividing 9m2 − 4m − 6 by 3m is shown. Which could be the next step?
Studentka2010 [4]
Idk i need an answer to lol

7 0
3 years ago
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