Question

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

Answer 1

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

What is a complex number?

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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