Question 713186
{{{(-i)^42}}}
First, we can make things easier if we separate the "-" from the "i". Using the fact that -i = -1*i and a rule for exponents, {{{(a*b)^n = a^n*b^n}}} we can rewrite the expression as:
{{{(-1)^42*i^42}}}
Since (-1)*(-1) = 1 and since {{{(-1)^42}}} is just 21 pairs of (-1)*(-1), {{{(-1)^42 = 1}}} So the expression is now down to:
{{{i^42}}}<br>
Since {{{i = sqrt(-1)}}}, {{{i^2 = -1}}}. And since {{{i^4 = (i^2)^2}}}, {{{i^4 = (-1)^2 = 1}}} Since {{{i^42}}} is 10 sets of {{{i^4}}} and one {{{i^2}}}, {{{i^4 = -1}}}:
{{{i^42 = (i^4)^10*i^2 = 1^10*(-1) = -1}}}<br>
So the answer to the problem is B (None).