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Question Number 139192 by EnterUsername last updated on 23/Apr/21

$$\mathrm{If}{z}_1\mathrm{and}{z}_2\mathrm{are}\mathrm{complex}n\mathrm{th}\mathrm{roots}\mathrm{of}\mathrm{unity}\mathrm{which}\mathrm{sub}-$$$$\mathrm{tend}\mathrm{right}\mathrm{angle}\mathrm{at}\mathrm{the}\mathrm{origin},\mathrm{then}n\mathrm{must}\mathrm{be}\mathrm{of}\mathrm{the}\mathrm{form}$$$$\left(\mathrm{A}\right)4\mathrm{K}+1\left(\mathrm{B}\right)4\mathrm{K}+2$$$$\left(\mathrm{C}\right)4\mathrm{K}+3\left(\mathrm{D}\right)4\mathrm{K}$$

Answered by mr W last updated on 24/Apr/21

$$\frac{2\pi }{n}\times k=\frac{\pi }{2}$$$$\Rightarrow n=4k$$

Commented by EnterUsername last updated on 24/Apr/21

$$\mathrm{OK}\mathrm{thanks}!$$

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