Question

Imaginary Numbers
Simplify
i 9

Answer 1

Please help!

Answer 2

That is simplified isnt it?

Answer 3

oh also it i^9

Answer 4

ah. ok then so

1^2 = -1 right

Answer 5

simplified version has to be i

Answer 6

Aww idk this kind of confusing me

Answer 7

(i^2)^4 . i
(-1)^4 . i
1i

Answer 8

(i^2)^4 . i
(-1)^4 . i
1i

Answer 9

any variable equals 1 automatically

Answer 10

Do you get it?

Answer 11

Basically take out an i^2 first so that you work with -1.

I.e i^4 = (i^2)^2

so now you have (-1)^2
=
1.

Do you understand up to there?

Answer 12

KIND of so it 1? a little ...

Answer 13

if there is no value to a variable it becomes a 1.

Answer 14

then the i Crossout ?

Answer 15

\[i^9=i^{4 \cdot 2 +1}=i^{4 \cdot 2} \cdot i^1=(i^4)^2 \cdot i=(1)^2 \cdot i\]
\[=1 \cdot i=i\]

Answer 16

pattern is
\[i^0=1\]
\[i^1=i\]
\[i^2=-1\]
\[i^3=-i\]
\[i^4=1\] and so on. so your real job is to take the integer remainder when you divide the power by 4. for example
\[i^{103}=i^3=-i\]

Answer 17

ohhhh i see !!! kk thank u that make sense !!!

Answer 18

yw