Ask Uncle Colin: A Complex Conundrum | Colin

Dear Uncle Colin,

I’m told that $z=i$ is a solution to the complex quadratic $z^2 + wz + (1+i)=0$, and need to find $w$. I’ve tried the quadratic formula and completing the square, but neither of those seem to work! How do I solve it?

– Don’t Even Start Contemplating A Robust Trial & Error Solution

Hello, DESCART&ES, and thank you for your message!

You’ll kick yourself. You’re told that when $z=i$, the equation holds, so your starting point should be substituting $z=i$ into the equation and seeing what happens.

You get $-1 + wi + 1 + i = 0$, so $w=-1$.

For the record,…

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