SOLUTION: ok, i just DONT understand imaginary numbers in problems! i really need help! heres a problem: 7i^3 + 8i^12 +9i^17 -5i^16 = ?
PLEASE HELP! i dont know what to do with the number
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Question 26058: ok, i just DONT understand imaginary numbers in problems! i really need help! heres a problem: 7i^3 + 8i^12 +9i^17 -5i^16 = ?
PLEASE HELP! i dont know what to do with the numbers in front...!!!
Found 2 solutions by venugopalramana, Earlsdon:
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
7i^3 + 8i^12 +9i^17 -5i^16 =
PLEASE NOTE THE FOLLOWING
I=I
I^2=-1
I^3=I^2*I=-I
I^4=(I^2)^2=(-1)(-1)=1
HENCE IN GENERAL
(I)^EVEN POWER = -1 OR +1..IT IS +1 IF THE POWER IS DIVISIBLE BY 4 OTHER WISE -1
(I)^ODD POWER = I OR -I ....IT IS +I IF THE POWER LESS ONE IS DIVISIBLE BY 4 OTHER WISE -I...
SO NOW YOU CAN DO THE PROBLEM I THINK ..LET US SEE
7i^3 + 8i^12 +9i^17 -5i^16 = -7I+8+9I-5=3-2I...OK...CLEAR?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Imaginary numbers: In math, the lower-case letter i is used to stand for the square root of -1, thus:
If you multiply i times i or this is the same as multiplying = -1 so you can see that
Now if you keep doing this, that is, find ,,, you begin to see a definite pattern:
=
= =
=
= =
= ...and so on.
Do you see it? Sometimes it's helpful to constuct a table for the values of for different values of n:
n----
--------------
1.....i
2....-1
3....-i
4.....1
5.....i
6....-1
7....-i
8.....1
9.....i
10...-1
11...-i
12....1
and so on
As for the number in front of the i's in your problem, you just multiply by that number. For example:
=
= 8
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