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If-z-1-and-z-2-are-complex-nth-roots-of-unity-which-sub-tend-right-angle-at-the-origin-then-n-must-be-of-the-form-A-4K-1-B-4K-2-C-4K-3-D-4K-




Question Number 139192 by EnterUsername last updated on 23/Apr/21
If z_(1 )  and z_2  are complex nth roots of unity which sub-  tend right angle at the origin, then n must be of the form  (A) 4K+1                   (B) 4K+2  (C) 4K+3                   (D) 4K
$$\mathrm{If}\:{z}_{\mathrm{1}\:} \:\mathrm{and}\:{z}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{complex}\:{n}\mathrm{th}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{which}\:\mathrm{sub}- \\ $$$$\mathrm{tend}\:\mathrm{right}\:\mathrm{angle}\:\mathrm{at}\:\mathrm{the}\:\mathrm{origin},\:\mathrm{then}\:{n}\:\mathrm{must}\:\mathrm{be}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{4K}+\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{4K}+\mathrm{2} \\ $$$$\left(\mathrm{C}\right)\:\mathrm{4K}+\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{4K} \\ $$
Answered by mr W last updated on 24/Apr/21
((2π)/n)×k=(π/2)  ⇒n=4k
$$\frac{\mathrm{2}\pi}{{n}}×{k}=\frac{\pi}{\mathrm{2}} \\ $$$$\Rightarrow{n}=\mathrm{4}{k} \\ $$
Commented by EnterUsername last updated on 24/Apr/21
OK thanks!
$$\mathrm{OK}\:\mathrm{thanks}! \\ $$

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