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# sanity check

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(a + bi)/(c + di) * (c - di)/(c - di) = (ac - bd)/(c^2 + d^2) - ((ad + bc)/(c^2 + d^2))*i and... 1 / (a + bi) * (a - bi)/(a - bi) = a/(a^2 + b^2) - (b/(a^2+b^2))*i Yes? I''m reading Tricks of the 3D Game Programming Guru''s and I''m in the complex math section.. however the book does not get the same answers for the identities as I do... am I doing something wrong, or is the book dumb?

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1 ==> (a + b)(c - d)i / (c^2 - d^2) since i^2 = -1
2 ==> (a - bi) / (a^2 - b^2)

blah blah blah.

[edited by - Chris Hare on May 17, 2004 8:28:17 PM]

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Yes, but the idea was to put it in proper complex form, that is, a + bi, or the seperated real and imaginary parts.

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Chris Hare, you''re wrong. The denominators are correct as they are, i.e. a2 + b2, because they are (a + bi)(a - bi) = a2 - (bi)2 = a2 + b2. Dovyman, you have some sign errors in your numerators. They should be

(a + bi)/(c + di) = [(ac + bd) / (c2 + d2)] + [(bc - ad) / (c2 + d2)]*i

1/(a + bi) = [a / (a2 + b2)] - [b / (a2 + b2)]*i

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I see. I was that eager to post first that I screwed up!

blah blah blah.

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Tricks of the gaming gurus does have some blaring math errors in the 2D transformations and physics chapters. It''s been a while since I''ve read the book, so I the only one that I really remember was the book having all the sin/cos/tan ratios messed up.

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