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Question Number 156400 by ajfour last updated on 10/Oct/21

Commented by ajfour last updated on 10/Oct/21

$$\mathrm{The}\mathrm{roots}\mathrm{of}\mathrm{f}\left(\mathrm{z}\right)={(\mathrm{z}-\mathrm{a})}^2+\mathrm{b}$$$$\mathrm{is}\mathrm{obtainable}\mathrm{by}\mathrm{the}\mathrm{welded}$$$$\mathrm{parabola}\mathrm{wires}(\mathrm{with}\mathrm{mutually}$$$$\mathrm{perpendicular}\mathrm{planes};\mathrm{upper}$$$$\mathrm{parallel}\mathrm{Re}-\mathrm{vertical},\mathrm{lower}$$$$\mathrm{one}\mathrm{parallel}\mathrm{to}\mathrm{Im}-\mathrm{Vertical}).$$$$\mathrm{Where}\mathrm{they}\mathrm{cross}\mathrm{f}\left(\mathrm{z}\right)=\mathrm{c}$$$$\mathrm{gives}\mathrm{z}=\mathrm{a}\pm \sqrt{\mathrm{c}-\mathrm{b}}★$$$$(\mathrm{Today}\mathrm{evening}\mathrm{i}\mathrm{imagined}\mathrm{this}!)$$$$...........................................$$

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