Respuesta :
We have to find the value of the expression [tex]i^{233}[/tex]
We know that the below values.
[tex]i^2=-1\\i^4=1[/tex]
Hence, in order to find the value of the given expression, we can first rewrite it in terms of [tex]i^4[/tex]
[tex]i^{233}=(i^4)^{58}\cdot i[/tex]
Now, we know that [tex]i^4=1[/tex]
Hence, we have
[tex]i^{233}=(1)^{58}\cdot i[/tex]
[tex]i^{233}=1\cdot i[/tex]
[tex]i^{233}=i[/tex]
C is the correct option.
The value of [tex]i ^{233}[/tex] is [tex]i[/tex].
Given to us
- [tex]i ^{233}[/tex]
What is the value of [tex]i ^{233}[/tex]?
We know the value of iota(i ) is equal to √-1.
therefore, the expression can be written as,
[tex]i^{233} = (\sqrt{-1})^{233}[/tex]
It can be furthered written as,
[tex]i^{233} = (\sqrt{-1})^{233}\\\\[/tex],
Using the exponential rule [tex]x^a \times x^b = x^{(a+b)}[/tex]
[tex]i^{233} = (\sqrt{-1})^{232} \times (\sqrt{-1})\\\\[/tex]
Using [tex](x^a)^b =x^{ab}[/tex],
[tex]i^{233} = [(\sqrt{-1})^2]^{116} \times (\sqrt{-1})\\\\i^{233} = (-1})^{116} \times (\sqrt{-1})\\\\i^{233} = 1 \times (\sqrt{-1})\\\\i^{233} = 1 \times i\\i^{233} = i[/tex]
Hence, the value of [tex]i ^{233}[/tex] is [tex]i[/tex].
Learn more about the Exponential rule:
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