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Question Number 142537 by mathocean1 last updated on 01/Jun/21

$$\mathrm{Given}:$$$${\mathrm{z}}_1={\mathrm{e}}^{\mathrm{i}\frac{\pi }{3}}(\mathrm{z}+3)-3\mathrm{and}{\mathrm{z}}_2={\mathrm{e}}^{-\mathrm{i}\frac{2\pi }{3}}(\mathrm{z}-3)+3.$$$$\mathrm{Show}\mathrm{that}$$$$\frac{{\mathrm{z}}_2-\mathrm{z}}{{\mathrm{z}}_1-\mathrm{z}}=\mathrm{i}\sqrt{3}\frac{\mathrm{z}-3}{\mathrm{z}+3}$$

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