# Is this a new formula? If so, what is it called?

You are given the zero, 5-5i.

Therefore you also have 5+5i.

You would then multiply the two complex zeros to find the polynomial function.

I spent a while attempting to more effectively multiply the two zeros and came up with the following:

(x - a - bi)(x - a +bi) = (x^2 - (2a)x + (a^2 + b^2)

So, for our numbers on lines 1 and 2, our answer would be:

f(x) = x^2 - 10x + 26

Is the formula I "discovered" "(x - a - bi)(x - a +bi) = (x^2 - (2a)x + (a^2 + b^2)" a known formula, or did I truly discover it?

Any feedback is appreciated!

-John

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