Question

Which expression is equivalent to i 233? 1 –1 i –i

Answer 1

Step-by-step explanation:

i¹ = i

i² = i×i = -1

i³ = -1 × i = -i

i⁴ = -i×i = - -1 = 1

i⁵ = 1×i = i

...

so, when the exponent of i modulo 4 (the remainder when dividing by 4) = 0, then the result is 1.

= 1, then the result is i

= 2, then the result is -1

= 3, then the result is -i

233 modulo 4 = 1 (233/4 = 58, remainder 1).

so, the result is i (the third answer option).