Question

What happens to f(n) as n increases? f(n) = |(7 4i)n|

Answer 1

As n increases, the value of f(n) = |(7 4i)n| also increases.

Step-by-step explanation:

As n increases, the value of f(n) = |(7 4i)n| will also increase. This is because the absolute value function ensures that the result is always positive, and raising a complex number to a larger power will generally increase its magnitude. Let's take an example to illustrate this:

Let n = 1. In this case, f(n) = |(7 4i)1| = |7 4i| = √(7^2 + 4^2) = √65 ≈ 8.06.

Now, let n = 2. In this case, f(n) = |(7 4i)2| = |49 - 16i| = √(49^2 + (-16)^2) = √2521 ≈ 50.21.

As you can see, as n increases, the value of f(n) also increases.