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Question Number 21005 by Tinkutara last updated on 10/Sep/17

$$\mathrm{If}{z}_1=a+ib\mathrm{and}{z}_2=c+id\mathrm{are}\mathrm{complex}$$$$\mathrm{numbers}\mathrm{such}\mathrm{that}\mid z_1\mid =\mid z_2\mid =1\mathrm{and}$$$$\mathrm{Re}\left(z_1{\overline{z}}_2\right)=0,\mathrm{then}\mathrm{the}\mathrm{pair}\mathrm{of}\mathrm{complex}$$$$\mathrm{numbers}{\omega }_1=a+ic\mathrm{and}{\omega }_2=b+id$$$$\mathrm{satisfy}$$$$\left(1\right)\mid {\omega }_1\mid =1$$$$\left(2\right)\mid {\omega }_2\mid =1$$$$\left(3\right)\mathrm{Re}\left({\omega }_1{\overline{\omega }}_2\right)=0$$$$\left(4\right)\mid {\omega }_1\mid =2\mid {\omega }_2\mid$$

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