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2 years ago

For any number n>1 is |(3/4+2/3i)^n|

Mathematics

1 answer:

sasho [114]2 years ago

6 0

The for any number n>1 is |(3/4+2/3i)^n| greater than 1 after simplifying the complex number.

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number:

$= \rm |(\dfrac{2}{3}+\dfrac{3}{4}i)^n|\\\\\\= \rm |(\dfrac{8+9i}{12})^n|\\\\\\= \rm |\dfrac{(8+9i)^n}{12^n}|\\\\$

Here n>1

Plug n = 2

$= \rm |\dfrac{(8+9i)^2}{12^2}|\\\\$

= 145/144

= 1.0069

Which is greater than 1.

Thus, the for any number n>1 is |(3/4+2/3i)^n| greater than 1 after simplifying the complex number.

Learn more about the complex number here:

brainly.com/question/10251853

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Read 2 more answers

In a specific video game scenario, you are given 1,000 gold. You can either train marines to defend your base at 50 gold a piece

Sloan [31]

Answer:

The system is:

$50m+200u\leq 1,000$

$u\leq 3$

$u\geq 0$

$m\geq 10$

Step-by-step explanation:

The variables of your equations are:

$m=\text{number of marines}$

$u=\text{number of upgrades}$

The constraints, which become inequalities are:

1. The total cost cannot be greater than 1,000 gold

Cost of training m number of marines at 50 gold a piece:

$50m$

Cost of purchasing u number of research weapon upgrades at 200 gold per upgrade:

$200u$

Total cost:

$50m+200u$

The cost is limited to 1,000 gold that you are given:

$50m+200u\leq 1,000$

That is the first inequality of your system

2. The game allows a maximum of three upgrades:

This sets an upper bound for the variable:

$u\leq 3$

Add the reasonable constraint that the number of upgrades cannot no be negative:

$u\geq 0$

3. You know that you need at least ten marines trained to survive

This sets a lower bound for the variable:

$m\geq 10$

And those are all the four inequalities that form your system to describe the number of marines and the number of upgrades you can train/purchae in the game:

$50m+200u\leq 1,000$

$u\leq 3$

$u\geq 0$

$m\geq 10$

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3 years ago