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Friday, October 16, 2009

The dawning of the rest of our lives

Day off today. Returned my failed external hard drive to the retailer. Got my Pixar fix by seeing Up in 2D. Tried the new Grand Angus McDonald's burger (it almost lives up to the hype). Got 100% in the Macro problem set.

Mr Macro, marking my problem set, seemed a little confused by the following statement about the polynomial $1-\alpha L - \beta \gamma L^{2}$ in $L$:

If both roots are complex ($\alpha^{2}+4\beta\gamma < 0$; note this can only occur if $\beta \gamma < 0$), the real and imaginary parts of the roots are \[ \Re = \frac{\alpha}{-2\beta\gamma} \qquad \Im = \pm \frac{\sqrt{- \left( \alpha^{2} + 4\beta\gamma \right)}}{-2 \beta\gamma} \]

He circled the negative sign inside the square root in the expression for the imaginary part, wrote a long comment, then crossed it out and gave me full marks. I know my handling of complex numbers is always a little idiosyncratic (due to self-teaching), but I didn't think it was that odd.

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