Question

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

A. Greater than one
B. Less than one
C. Equal to one

Answer 1

Based on the calculations, for any number n > 1, $|(\frac{1}{2} + \frac{3i}{4} )^n|$ is less than one but not greater than or equal to one.

How to solve the equation?

First of all, we would simplify the equation by using the lowest common multiple (LCM) of the fractions as follows:

$|(\frac{2\;+\;3i}{4} )^n|$

By applying exponent rule, we have:

$(a.b)^n=a^n \times b^n\\\\|(\frac{(2\;+\;3i)^n}{4^n} )|\\\\|(\frac{(2\;+\;3i)^n}{(2^2)^n} )|$

By applying exponent power rule, we have:

$|(\frac{(2\;+\;3i)^n}{2^{2n}} )|$

Assuming n = 2, we have:

$|(\frac{(2\;+\;3i)^2}{2^{2\times 2}} )|\\\\|(\frac{(2\;+\;3i)^2}{2^{4}} )|\\\\|(\frac{-5\;+\;12i}{16} )|$

Therefore, for any number n > 1, $|(\frac{1}{2} + \frac{3i}{4} )^n|$ is less than one but not greater than or equal to one.

Read more on complex equations here: https://brainly.com/question/15007300

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