Answer:
The simplified given expression is [tex]i^{11}=-i[/tex]
Step-by-step explanation:
Given expression is [tex]i^{11}[/tex]
To simplify the given expression [tex]i^{11}[/tex] as below:
[tex]i^{11}=i^{10+1}[/tex]
[tex]=i^{10}.i^1[/tex] ( using the property [tex]a^{m+n}=a^{m}.a^{n}[/tex] )
[tex]=(i^2)^5.i[/tex] ( using the property [tex](a^m)^n=a^{mn}[/tex] )
[tex]=(-1)^5.i[/tex] ( since [tex]i^2=-1[/tex] )
[tex]=(-1).i[/tex] ( since power is odd so we get -1 )
[tex]=-i[/tex]
Therefore [tex]i^{11}=-i[/tex]
Therefore the simplified given expression is [tex]i^{11}=-i[/tex]
