Respuesta :
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:
[tex]= \rm |(\dfrac{2}{3}+\dfrac{3}{4}i)^n|\\\\\\= \rm |(\dfrac{8+9i}{12})^n|\\\\\\= \rm |\dfrac{(8+9i)^n}{12^n}|\\\\[/tex]
Here n>1
Plug n = 2
[tex]= \rm |\dfrac{(8+9i)^2}{12^2}|\\\\[/tex]
= 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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