lisa123
  • lisa123
(-i)^10
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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lisa123
  • lisa123
evaluate
denonakavro
  • denonakavro
The answer will be -1
lisa123
  • lisa123
yes I know but why...I get 1 when I work it out

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More answers

freckles
  • freckles
do you know i^4=1?
lisa123
  • lisa123
yes
freckles
  • freckles
\[\frac{10}{4}=2+\frac{2}{4} \\ 10=4(2)+2 \text{ just multpied 2 on both sides } \\ i^{10}=i^{4 \cdot 2 +2} =i^{4 \cdot 2} i^2 \text{ by law of exponents } \\ i^{10}=i^{4 \cdot 2 } i^2 =(i^4)^2 i^2 \text{ also by law of exponents } \\ \text{ recall } i^4=1 \\ i^{10}=(1)^2 i^2 =i^2 \] do you know what i^2 equals ?
freckles
  • freckles
\[i^{n}=i^{ \text{ remainder of } n \text{ divided by 4 }}\]
freckles
  • freckles
so in summary we know i^(10) will be i^2 since 10 divided by 4 gives a remainder of 2
freckles
  • freckles
and i^2=...
lisa123
  • lisa123
-1 @freckles
freckles
  • freckles
right
freckles
  • freckles
\[i^{10}=i^2=-1\]
lisa123
  • lisa123
like I undertand your work but what happens to the negative that was attached to the i
freckles
  • freckles
\[(-i)^{10}=i^{10}\] do you know why?
freckles
  • freckles
\[(-i)^{10}=(-1 \cdot i)^{10} =(-1)^{10} i^{10} \text{ also by law of exponents } \\ \text{ but } (-1)^{10}=?\]
freckles
  • freckles
another example: \[(-i)^{51}=(-1 \cdot i)^{51}=(-1)^{51} (i)^{51} =-1 (i)^{51}=-1 \cdot (i^{3})=-1 \cdot (i^{2} \cdot i) \\ =-1 ( -1 \cdot i) =(-1 \cdot -1)i=1i\]
lisa123
  • lisa123
ohhhhh is it b/c (-i)I^10 is raised to a positive root??? so the answer is 1
freckles
  • freckles
right if you had an odd power like the one in the example then you would have -1 *i^(51)
lisa123
  • lisa123
oh wow im stupid....I got confused b/c my teacher gave me an example with an odd exponent
freckles
  • freckles
oh
lisa123
  • lisa123
thank you! @freckles
freckles
  • freckles
np

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