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3 years ago

Simplify the expression (9 + 2i)(9 − 2i).

Mathematics

2 answers:

earnstyle [38]3 years ago

6 0

Answer:

81 - 4i^2

Step-by-step explanation:

(9 + 2i)(9 - 2i)

Multiply First number in First parentheses to the first number in the second set of parentheses.

Multiply first number in the first parentheses with the second number in the second parentheses.

So you'll have:

81 - 18i

Then multiply the second number from the first parentheses by the first number in the second parentheses.

And multiply the second number in first parentheses by the second number in the second parentheses.

So then you'll have:

81 - 18i + 18i - 4i^2

Combine like terms:

81 - 4i^2

Final answer is:

81 - 4i^2

mestny [16]3 years ago

5 0

Answer:

(9 + 2i)(9 − 2i) = 81 - 4i²

Step-by-step explanation:

a² - b² = (a + b)(a - b)

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How many ways can 6 people be chosen and arranged in straight line if there are 8 people to choose from? a. 48.b. 720.c. 20, 160

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Answer:

Step-by-step explanation:

This question bothers on permutation since we are to select a some people out of a group of people and then arrange in a straight line. If r object are to be arranged in a straight line when selecting them from n pool of objects. This can be done in nPr number of ways.

nPr = n!/(n-r)!

Selection of 6 people out of 8 people can therefore be done in 8C6 number of ways.

8P6 = 8!/(8-6)!

8P6 = 8!/2!

8P6 = 8*7*6*5*4*3*2!/2!

8P6 = 8*7*6*5*4*3

8P6 = 56*360

8P6 = 20,160

<em>Hence this can be done in 20,160 number of ways</em>

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3 years ago

A gallery has 25 paintings in its permanent collection, with display space for 10 at one time. How many different collections ca

Anastaziya [24]

You need to know in how many ways you can choose 10 out of 25 items when order does not matter. This is a combination problem.

$_{n}C_{r} = \dfrac{n!}{(n - r)!r!}$

$_{25}C_{10} = \dfrac{25!}{(25 - 10)!10!}$

$_{25}C_{10} = \dfrac{25 \times 24 \times 23 \times 22 \times 21 \times 20 \times 19 \times 18 \times 17 \times 16 \times 15!}{15! \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}$

$_{25}C_{10} = \dfrac{25 \times 24 \times 23 \times 22 \times 21 
\times 20 \times 19 \times 18 \times 17 \times 16}{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 
\times 2 \times 1}$

$_{25}C_{10} = \dfrac{23 \times 11 \times 20 \times 19 \times 2 \times 17}{1}$

$_{25}C_{10} = 23 \times 11 \times 20 \times 19 \times 2 \times 17$

$_{25}C_{10} = 3,268,760$

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