Given-z-1-e-i-pi-3-z-3-3-and-z-2-e-i-2pi-3-z-3-3-Show-that-z-2-z-z-1-z-i-3-z-3-z-3-

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

Given: z_1 =e^(i(π/3)) (z+3)−3 and z_2 =e^(−i((2π)/3)) (z−3)+3. Show that ((z_2 −z)/(z_1 −z))=i(√3)((z−3)/(z+3))

$$\mathrm{Given}: \\ $$$$\mathrm{z}_{\mathrm{1}} =\mathrm{e}^{\mathrm{i}\frac{\pi}{\mathrm{3}}} \left(\mathrm{z}+\mathrm{3}\right)−\mathrm{3}\:\mathrm{and}\:\mathrm{z}_{\mathrm{2}} =\mathrm{e}^{−\mathrm{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \left(\mathrm{z}−\mathrm{3}\right)+\mathrm{3}. \\ $$$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\frac{\mathrm{z}_{\mathrm{2}} −\mathrm{z}}{\mathrm{z}_{\mathrm{1}} −\mathrm{z}}=\mathrm{i}\sqrt{\mathrm{3}}\frac{\mathrm{z}−\mathrm{3}}{\mathrm{z}+\mathrm{3}} \\ $$

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Given-z-1-e-i-pi-3-z-3-3-and-z-2-e-i-2pi-3-z-3-3-Show-that-z-2-z-z-1-z-i-3-z-3-z-3-

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