Question 936945
a. Use the identity {{{i^2 = -1))) to compute the powers of {{{i}}} and complete the table.
Type your response here:
Power of i Result
{{{i^3=i^2*i=(-1)*i=-i}}}
{{{i^4=i^2*i^2=(-1)*(-1)=1}}}
{{{i^5=i^2*i^2*i=(-1)*(-1)*i=i}}}
{{{i^6=i^2*i^2*i^2=(-1)*(-1)*(-1)=-1}}}
{{{i^7=i^2*i^2*i^2*i=(-1)*(-1)*(-1)*i=-i}}}
{{{i^4n=(i^4)^n=(i^2*i^2)^n=((-1)*(-1))^n=1^n=1}}}
{{{i^(4n+1)=(i^4)^n*i=1*i=i}}}
{{{i^(4n+2)=(i^4)^n*i^2=1*(-1)=-1}}}
{{{i^(4n+3)=(i^4)^n*i^2*i=1*(-1)*i=-i}}}


b. Examine the pattern in the powers of {{{i}}} you wrote in the table, and create a rule for finding the value of large powers of {{{i}}}. Justify your answer. 

{{{b^n}}} is the product of multiplying {{{n}}} bases:

{{{b^n=b*b*b}}}.......{{{b }}} and  {{{b}}} is multiplied by {{{b}}}   {{{ n}}}  times

so,we can apply same rule if  {{{b= i^2}}} and we will have 

{{{(i^2)^n=i^(2n)=i^2*i^2}}}.......{{{i^2 }}}......   {{{n}}} times