Question

simplify i^36

Answer 1

\[i^{36}=i^{4(9)}=(i^4)^9\]
What is i to the fourth?

Answer 2

And then do whatever that is to the 9th power and you are done :)
But no -1 is not the answer

Answer 3

im confused @myininaya . please explain further ?

Answer 4

4*9 is 36
I always divide the exponent by 4

Like here are some examples:

\[i^5=i^{4(1)+1}=i^4i=1(i)=i\]
\[i^6=i^{4(1)+2}=i^4i^2=(1)(-1)=-1\]
\[i^7=i^{4(1)+3}=i^4i^3=(1)i^3=i^3=-i\]
\[i^8=i^{4(2)}=(i^4)^2=(1)^2=1\]
\[i^35=i^{4(8)+3}=i^{4(8)}i^3=(i^4)^8i^3=(1)^8i^3=(1)(i^3)=i^3=-i\]

Answer 5

oops that last one is\[ i^{35}\]

Answer 6

\[i=\sqrt{-1}\]\[i ^{2}=-1\]

Answer 7

so what is the right one ?

Answer 8

what do you mean?

Answer 9

You can't simplify what I wrote for you above?

Answer 10

\[i ^{2}\times i ^{2}=i ^{4}=-1\times-1=1\]Now look at my ininaya very first post.

Answer 11

im just gonna stick with -1 lmao

Answer 12

That will be incorrect

Answer 13

I will make it easy for you
Take the exponent
And divide it by 4
Look at the reminder
If remainder 1, then the answer is i^1=i
If remainder 2, then the answer is i^2=-1
If remainder 3, then the answer is i^3=-i
If remainder 0, then answer is i^0=1

Answer 14

The question has been closed. The pursuit of knowledge was short one.