ShmoopTube

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Okay say t shmoop er's If i equals the square

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root of negative one it's A conceptual thing Which of

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the following is equal to the complex Number four plus

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five high over six minus two i this complex number

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is actually a lot more complex iq ated than it

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looks wait that's in the world is anyway The strategy

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here involves conjure gets both the numerator and denominator need

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to be multiplied by the country get of the denominator

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right So the denominators country it looks exactly the same

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as the denominator except the sign for two i switch

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is on ly the sign for the second term changes

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and if you didn't show up for school toe learn

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that this day Well then you're out of luck So

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the sign for six days positive and that negative too

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i becomes positive too I also that fraction more multiplying

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by well doesn't change the overall expressions value because the

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numerator and denominator are the same So we actually multiplied

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by one So that gets us this equation for plus

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five i over six minus two times six plus two

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eye over six plus two i okay were conjugating in

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the denominator The two i terms cancel out Kind of

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like a difference of squares does and there's one real

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term in a nice square term and because i squared

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is negative one and pretty much by definition The denominators

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simplifies to a real term so we just replace each

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ice square term with negative one and then our equation

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goes teo twenty four plus eight i plus thirty i

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plus ten i squared over was that thirty six plus

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twelve i minus twelve i minus four i squared so

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we're just playing across all right and then we just

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combine like terms and it gets us twenty four plus

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thirty eight i minus ten thirty six minus clooney thinkit's

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forty and then the final reduction fourteen plus thirty eight

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i over forty There we go Well this fraction can

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be split into two fractions because the denominator is now

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one term giving us our answer of seven twentieth plus

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nineteen i over twenty it's d well don't split the

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fraction in the question into two different fractions like air

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b did That strategy only works if the denominator is

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one term which is not the case until we multiplied

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by the conjugated So yeah it was a hard problem 00:02:16.08 --> [endTime] if you got it Q does

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