McDougal Littell Algebra 2
Lesson 5.4: Complex Numbers
*Challenge*
p.280 #100
Powers of i
Describe the pattern you observed in the table.
Verify that the pattern continues by evaluating the next four powers of i.
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16 years ago
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Hola. I'm posting a comment for the extra credit! So ya..
pg. 280 #100
b) I believe that there is a pattern in this sequence. The pattern is i,-1,-i,1 and continues as such... I think that's all we needed to do so.. Goodnight everyone.
I can't find the Algebra 2 blog so I looked on here and I saw the two comments already. I think there is a pattern and it is i, -1, -i, 1 so that's it for me.
Pg.280 #100
B) The patterning sequence here is i, -1, -i, 1 and countinues where larger numbers can be found by dividing by 2,3, or 4 and using the remainder to find the answer.
ex. credit pg.280 #100 the pattern i noticed is that every 4 exponent powers the pattern repeats itself. and it was i,-1,-i,1. and the signs pattern i saw was pos., neg., neg., pos. thats all. btw, im sick and not feeling well so probally wont attend school tomm. sorry,bye and good night.
pg.280 #100 b) I'm sure the pattern is i, -1, -i, 1 and that is my final answer.
Pg.280 #100
B) The pattern is i, -1, -i, 1, i, -1, -i, 1 etc,
this is supported algebraically because
you know that √-1 = i.
i^1 is i x 1. which equals i.
then i^2 is i x i. or √-1 x √-1 which equals -1.
then i^3 is i x i x i. or √-1 x √-1 x √-1 which is 1√-1 or simply i.
and the pattern contines.
goodnight. (:
oops ,sorry i made a mistake on the 3rd one.
i^3= √-1 x √-1 x √-1 which is -1√-1
or just -i
pg 280 #100
b) The pattern i found (after reworking these since I got it wrong the fist time) was i, -1, -i, then 1, and repeats like that.
Giovanni, sorry you're not feeling well. Remember to check the calendar at the bottom of the website to keep up with what you missed. You'll find your returned homework in the "2nd OUT" folder.
Adam...What are you doing up at 4 in the morning???
Extra credit is not more important than sleep.
The pattern i observed in the table was that since you already knew what i, i^2 and i^3 was breaking the numbers down to multiples of either 1, 2,or 3 and then substituting in the value i was able to come up with a value for i to the power of whatever the number, for example i^9 is i, i^10 is -1, i^11 is -i and i^12 is 1.
Helo, I want some extra credit!
I believe the pattern occurs every four (4) numbers. the patern is i, -1, -i, 1... Well that's all i got and thanks a lot!
Mortatha A.
hello im posting a comment for extra credit
so....pg 280 # 100....
The pattern that I observed is that i to the power of 2=-1, therefore every time a number is multiplied by i to the power of 2 it is multiplied by -1. This makes the pattern i, 1, -i, 1, i etc.
ex. ixi to the power of 2= ix-1( or i to the power of 3)
k bye
Extra Credit pg. 280 #100.
B)I noticed a pattern after doing the first 4. The pattern is i, -1, -i, 1. Therefore, i to the 9th power is i, i to the 10th power is -1, i to the 11th power is -i, and i to the 12th power is 1.
Part B #100 pg. 280:
I observed a pattern in the powers of i as i, -1, -i, and 1, where i is the value of i^1. The pattern continues to repeat like so as the powers of i increases, shown in the next four powers of i:
i^5 = i
i^6 = -1
i^7 = -i
i^8 = 1
pg. 280 #100
The pattern in the problem is i, -1, -i, and 1.
For example:
i^9 =i
i^10 =-1
i^11 =-i
i^12 =1
I just saw this today. Here is what I wrote for part B on powers of i.
The pattern that I see in this chart is that it follows a four number pattern. That pattern is i,-1,-i and then 1. After that, it restarts at the beginning of the pattern for the next 4 powers in the chart.
The pattern was i,-1,-i,1 and the signs pattern was pos., neg., neg., pos.
The pattern for this problem is that i, -1, -i,1. Switching off between these four numbers in this pattern after each exponential increase.
Adnan
pg.280 #100 the pattern in this sequence occurs every four numbers and is i,-1,-i,1,
Haha! Ms, i usually get up at four. I figured since i was up, i might as well get xtra credit :)
p. 280 #100
b.) Since i x i = -1, i^3 = i x i^2 = -1(i) = -1.
i^4 = i^2 x i^2 = (-1)(-1) = 1
Every other even exponent is positive one. One way to find out is by dividing the exponent by 2 and if it is an even number, it is a positive. If the outcome is odd, it is a negative. Odd exponents are multiplied by i.
So i^79 would be -1i because the exponent is odd, which multiplies i to -1; and 78/2 = 39 so it is negative 1.
That's what I think the pattern is. Goodbye :D
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