Question Number 139192 by EnterUsername last updated on 23/Apr/21
$$\mathrm{If}\:{z}_{\mathrm{1}\:} \:\mathrm{and}\:{z}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{complex}\:{n}\mathrm{th}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{which}\:\mathrm{sub}- \\ $$$$\mathrm{tend}\:\mathrm{right}\:\mathrm{angle}\:\mathrm{at}\:\mathrm{the}\:\mathrm{origin},\:\mathrm{then}\:{n}\:\mathrm{must}\:\mathrm{be}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{4K}+\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{4K}+\mathrm{2} \\ $$$$\left(\mathrm{C}\right)\:\mathrm{4K}+\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{4K} \\ $$
Answered by mr W last updated on 24/Apr/21
$$\frac{\mathrm{2}\pi}{{n}}×{k}=\frac{\pi}{\mathrm{2}} \\ $$$$\Rightarrow{n}=\mathrm{4}{k} \\ $$
Commented by EnterUsername last updated on 24/Apr/21
$$\mathrm{OK}\:\mathrm{thanks}! \\ $$