For any number n>1 is |(3/4+2/3i)^n|
1 answer:
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:
Here n>1
Plug n = 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.
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The function exists in a parabola.
The axis of symmetry of a parabola exists at the midpoint between the two real roots.
The roots exist the solutions of H(t) = 0
To estimate the roots equation exists
Factor t(-16t + 64) = 0
t = 0 and -16t + 64 =0
-16t + 64 = 0
t = 64 / 16 = 4
t = 4
Then the two roots are t = 0 and t = 4, and the axis of symmetry exists
t = (0+4)/2 = 4/2 = 2
<h3>How to estimate the axis of symmetry?</h3>The axis of symmetry exists at t = 2.
It represents the time at which the ball is at the higher point, the maximum height.
You can find the maximum height replacing t = 2 in the function H(t)
= 64 feet.
And you can also deduce that the second part of the flight will take 2 seconds, for a total flight time of 4 seconds.
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