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Question Number 19687 by Tinkutara last updated on 14/Aug/17

$$\mathrm{Let}{z}_1,z_2,z_3\mathrm{be}\mathrm{three}\mathrm{vertices}\mathrm{of}\mathrm{an}$$$$\mathrm{equilateral}\mathrm{triangle}\mathrm{circumscribing}\mathrm{the}$$$$\mathrm{circle}\mid z\mid =\frac{1}{2}.\mathrm{If}{z}_1=\frac{1}{2}+\frac{\sqrt{3}i}{2}\mathrm{and}{z}_1,$$$$z_2,z_3\mathrm{are}\mathrm{in}\mathrm{anticlockwise}\mathrm{sense}\mathrm{then}{z}_2\mathrm{is}$$

Answered by ajfour last updated on 14/Aug/17

$${\mathrm{z}}_2={\mathrm{z}}_1{\mathrm{e}}^{\mathrm{i}2\pi /3}={\mathrm{e}}^{\mathrm{i}\pi /3}.{\mathrm{e}}^{\mathrm{i}2\pi /3}={\mathrm{e}}^{\mathrm{i}\pi }=-1.$$

Commented by Tinkutara last updated on 14/Aug/17

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

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