Question
4 times Find the value of i^703 . 4 x & A & 1 4 x & B & 1 4 x & C & -1 4 x & D & -1
Answer
4.5
(324 Votes)
Meredith
Elite · Tutor for 8 years
Answer
# ExplanationTo find the value of
, we need to understand the properties of the imaginary unit
. The imaginary unit
is defined as
. The powers of
follow a cyclical pattern:
From this, we see that the powers of
repeat every 4 terms. Therefore, to find
, we can use modular arithmetic to determine the equivalent power within the first cycle of 4 terms.We calculate the remainder when 703 is divided by 4:
Performing the division:
Thus,
This means that
is equivalent to
. From the cyclical pattern, we know:
Therefore,
.# AnswerC