Question

Which expression is equivalent to i233?

Answer 1

We have to find the value of the expression i^{233}i
233

We know that the below values.

$\begin{lgathered}i^2=-1\\i^4=1\end{lgathered}$
i
2
=−1
i
4
=1
​

Hence, in order to find the value of the given expression, we can first rewrite it in terms of i^4i
4

i^{233}=(i^4)^{58}$\cdot ii$
233
=(i
4
)
58
⋅i

Now, we know that i^4=1i
4
=1

Hence, we have

i^{233}=(1)^{58}$\cdot ii$
233
=(1)
58
⋅i

i^{233}=$1\cdot ii$
233
=1⋅i

i^{233}=ii
233
=i

Answer 2

i^1 = i 
i^2= -1 
i^3 = i *-1 = -i