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All numbers are in our imagination…

August31

…even Imaginary Numbers! Yes, we were all taught in school that you cannot take the square root of a negative number. Quite right! Well, not quite right!! Actually, around a few hundred years ago (early 1600’s), someone (Ren√© Descartes actually)¬†thought it might be really useful to be able to find the square root of a negative number, so he thought up the letter “i” to do this for him (“i” for an imaginary number is, after all, pretty imaginative?)”

i = sqrt(-1)

You can imagine the mathematical confusion that these imaginary numbers caused!

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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