Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.

QUESTION

How do you simplify ##i44 + i150 - i74 - i109 + i61##?

1

We have, ##i^1=i## ##i^2= -1## ##i^3 = i^2 xx i = -i## ##i^4 = i^2 xx i^2 =(-1)^2 xx (-1)^2 = 1## ##i^5 = i^4 xx i = 1 xx i =i## ##i^6 = i^4 * i^2 = 1 * -1 = -1## ##i^7 = i^4 * i^3 = 1 * -i = -i ## ##i^8 = i^4 * i^4 = 1 * 1 = 1##

Now, ##i^44 = (i^4) ^11 = (1)^11 = 1## ##i^150 = (i^4)^37 * i^2 = i^2 = -1## ##i^74 = (i^4)^18 * i^2 = i^2 = -1## ##i^109 = (i^4)^27 * i^1 = i ## ##i^61 = (i^4)^15 * i^1 = i ##

Finally, ##i^44 + i^150 - i^74 - i^109 + i^61## ##=(1) + (-1) - (-1) - (i) + (i)## ##=1 - 1 + 1 - i + i## ##= 1 ##

Show more
LEARN MORE EFFECTIVELY AND GET BETTER GRADES!
Ask a Question