Question

Which expression is equivalent to i233?
A) i
B) 1
C) -i
D) -1

Answer 1

Answer:

option (A) is correct

Step-by-step explanation:

$concept: \\\\i^{4n}=1 \\\\i^{4n-1}=-i \\\\i^{4n-2}=-1 \\\\i^{4n-3}=i \\\\where,\:i=\sqrt{-1} \\\\Now, \\\\i^{233}=i$

Answer 2

We know, i^2= -1

i^3 = i *-1 = -i

i^4= -1*-1= 1

Though 233 isn't divisible by 4, but the closest divisible by 4 is the number 232.

Alternatively, i^232 would be the same as i^4, which is 1

So, i^(232+1)

= i^(4*58)+1

Hence, we get i^1 which is equal to i.

So, the correct option is A) i

Hope it helps!

#MVB