SOLUTION: {{{i^1= i}}} {{{ i^5 = i}}} {{{i^2= -1 }}} {{{ i^6 = -1}}} {{{i^3= -i }}} {{{ i^7= -i}}} {{{i^4= 1 }}} {{{ i^8 = 1}}} I am supposed to use the above pa

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Question 79349:

I am supposed to use the above pattern to simplify the powers of i.

Please help
Please help
Found 2 solutions by chitra, josmiceli:
Answer by chitra(359) (Show Source):
You can put this solution on YOUR website!
Here we are given the values of i till = 1

Now to find this can be written as:

This can be written as:

Lets now find the value of from the given data:

= 1

=

=

= i

=

= i * i

=

= -1

Similarly the rest are also found out.

= -i

= 1

= i

Thus the value of = i

And we know that = i

Thus, =

=

= i

Hence, the solution.

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2nd method

Or we can also find the value of =

=

=

= i

Now 65 = 13 * 5

=

=

= i

Hence, the solution.

Regards
Chitra
Online MAth tutor
www.knowledgeonlineservices.com

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!

The easiest property to make use of is
because every time you
multiply it times itself, you still get 1

Remember you ADD the exponents in each case, so

Think of as multiplied times itself a certain
number of times and multiply that by whatever factor is left over
and 1 remainder
What you've got is or

So, answer