SOLUTION: 9) the expression i to the 25 power is eqivalen to? a) -i b)1 c)i d)-1 10) What does the expression i to 100th power + i to the 101 power + i to the 102 power equal? a) 1

Question 252737: 9) the expression i to the 25 power is eqivalen to?
a) -i
b)1
c)i
d)-1
10) What does the expression i to 100th power + i to the 101 power + i to the 102 power equal?
a) 1
b)i
c)-i
d)-1
11) What is the sum of 5-3i and the conjugate of 3+2i?
12) The expression 3i(2isquared-5i) is eqivalent to?
a)15-5i
b)-15-5i
c)8+5i
d)2-5i

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
9) the expression i to the 25 power is eqivalen to?
a) -i
b)1
c)i
d)-1
The powers of i are cyclic mod 4, meaning there are 4 possibilities.
exp...value
1....i
2....-1
3....-i
4....+1
Then it repeats. For the 25th power, divide 25 by 4 and get the remainder. That's 25 mod 4, or in Excel, mod(25,4) and the remainder is 1.
i^1 = i
--------
10) What does the expression i to 100th power + i to the 101 power + i to the 102 power equal?
a) 1
b)i
c)-i
d)-1
i^100 = 1
1^101 = i
i^102 = -1
---------- Add
= i
---
11) What is the sum of 5-3i and the conjugate of 3+2i?
The conjugate of 3+2i is 3-2i
5-3i
3-2i
----- Add
8-5i
--------------
12) The expression 3i(2isquared-5i) is eqivalent to?
a)15-5i
b)-15-5i
c)8+5i
d)2-5i
3i*(2i^2 - 5i)
= 3i*(-2 - 5i)
= -6i - 15i^2
= -6i - 15*(-1)
= 15 - 6i

RELATED QUESTIONS
please explain how to simplify... i to the 100th... (answered by jim_thompson5910)

okay so i have aquestion that reads: If Log(x+1)+log(x-1) = 5, then what expression is... (answered by edjones)

simplify (1+i)to the 2nd... (answered by sdmmadam@yahoo.com)

could you please explain how to solve this problem? simplify... i to the 100th... (answered by Mathtut)

10 to the power of (3) + 10 to the power of (5) = ? a) 10 to the power of (8) b) 10... (answered by Alan3354)

what is i to the 235th... (answered by whty89,bmauger)

what is i to the 50th power? (answered by rfer)

what is 'i' to the 233... (answered by stanbon)

what is i to the 27th... (answered by ewatrrr)