Question 252737
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
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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
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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
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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