Let OA.$$OB=1$$ and let O, A, B, be three collinear points. if O and B represent the complex numbers $$0$$ and z, then A represents:

Question

Let OA.$$OB=1$$      and  let O, A, B, be three collinear points. if O  and B represent the complex numbers $$0$$ and z, then A represents:

Infinity Learn · Accepted Answer

Given that OA.$$OB=1$$            ⇒|$$z1$$−$$0$$|.|z−$$0$$|$$=1$$⇒|$$z1$$|$$=1$$|z|....................(1)     Also, $$amp(z1$$−$$0z$$−$$0)=0$$  or  π⇒$$amp(z1z)=0$$  or  π     ⇒$$amp(z1)$$−$$amp(z)=0$$  or  π     ⇒$$ampz1=amp$$ z or $$amp(z)+$$π     Let θ      be the amp of $$z1$$     ,then $$z1$$     $$=$$|$$z1$$|$$($$$$cos$$θ$$+isin$$θ$$)$$                                                                $$=1$$|z|$$($$$$cos$$θ$$+isin$$θ$$)$$                 [using  $$eq(1)$$]                                                           $$=1$$|z|$$2$$|$$z1$$|$$($$$$cos$$θ$$+isin$$θ$$)=1$$|z|$$2($$±$$z)$$.                                                                $$=$$±zzz¯$$=$$±$$1z$$                ∴$$z1=1z$$  or  −$$1z$$

Let $O A . O B = 1$ and let O, A, B, be three collinear points. if O and B represent the complex numbers 0 and z, then A represents:

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Let OA.OB=1 and let O, A, B, be three collinear points. if O and B represent the complex numbers 0 and z, then A represents:

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Let $O A . O B = 1$ and let O, A, B, be three collinear points. if O and B represent the complex numbers 0 and z, then A represents: