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Question Number 19629 by Tinkutara last updated on 13/Aug/17

$$\mathrm{If}\mid z\mid =2,\mathrm{then}\mathrm{the}\mathrm{points}\mathrm{representing}$$$$\mathrm{the}\mathrm{complex}\mathrm{numbers}-1+5z\mathrm{will}\mathrm{lie}$$$$\mathrm{on}\mathrm{a}$$$$\left(1\right)\mathrm{Circle}$$$$\left(2\right)\mathrm{Straight}\mathrm{line}$$$$\left(3\right)\mathrm{Parabola}$$$$\left(4\right)\mathrm{Ellipse}$$

Answered by ajfour last updated on 13/Aug/17

$$\mathrm{x}+\mathrm{iy}=-1+5\times {2\mathrm{e}}^{\mathrm{i}\theta }$$$$\mathrm{x}-\mathrm{iy}=-1+5\times {2\mathrm{e}}^{-\mathrm{i}\theta }$$$$(\mathrm{x}+1+\mathrm{iy})(\mathrm{x}+1-\mathrm{iy})=100$$$${(\mathrm{x}+1)}^2+{\mathrm{y}}^2={10}^2$$$$\mathrm{They}\mathrm{lie}\mathrm{on}\mathrm{a}\mathrm{circle}\mathrm{then}.\left(1\right).$$

Commented by Tinkutara last updated on 13/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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