SOLUTION: Simplify: First Question: i^2522 Second Question: 16/2i

Question 28839: Simplify:
First Question:
i^2522

Second Question:
16/2i
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
Simplify:
First Question:
i^2522
Second Question:
16/2i
First Question:
i^2522
2522 = 630X4 + 2
i^2522 = (i)^ (630X4 + 2)
=[(i)^(630X4)] X[(i)^2 ] [using formula (a)^(mn+k) = (a)^(mn) X(a)^k]
=[(i^4)^(630)]X(-1) [using (a)^(mn) = [(a)^n]^m ]
=[(1)^630]X(-1)
=1X(-1)
= -1
Note: 2522 on division by 4 gives remainder 2
Why should we divide by 4?
Because i^4= 1 [ i^1= i, i^2=-1,i^3 = (-1)Xi = -i and i^4 = (i^2)^2 = (-1) ^2 = +1]
And (1)^(any integer) = 1
Second Question:
(16/2i) =[(16/2i)]X[(i)/(i)] (multiplying nr and dr by (i) and canceling 2]
=(8Xi)/(iXi)
=8i/(i^2)
=8i/(-1)
= -8i
Note: Why should we multiply nr and dr by (i)?
Because i is complex and i itself is the real- izing factor
that is, i is the factor which when multiplied by the complex number i gives the real number (i^2) = -1
RELATED QUESTIONS
simplify:... (answered by )

simplify 1-i /... (answered by user_dude2008)

Simplify (5-i) -... (answered by geometryworm7271)

Simplify (4+i) (5-2i) (answered by jim_thompson5910)

I have a question that I (think) I got the correct answer, but it makes no sense in the... (answered by stanbon)

My first questions is : Simplify the following equations. 6 over radical 15... (answered by ewatrrr)

Simplify the expression -5+i over 2i -5+i ______... (answered by MathLover1)

Will you please solve this question 1 / i... (answered by Alan3354)

This is a 3 part question but i already answered the first part on my own. The other two... (answered by stanbon,RAY100)