Let A 1 ( Z 1 ) , A 2 ( Z 2 ) be the adjacent vertices of a regular polygon. If Re ( Z 1 ) lm ( Z 1 ) = 1 − 2 , then the number of sides of the polygon are

Question

Let A 1 ​ ( Z 1 ​ ) , A 2 ​ ( Z 2 ​ ) be the adjacent vertices of a regular polygon. If Re ( Z 1 ​ ) lm ( Z 1 ​ ​ ) ​ = 1 − 2 ​ , then the number of sides of the polygon are

TestHub · Accepted Answer

Let z 1 ​ = r e i θ , Z ˉ 1 − i θ ​ = r e − i θ , Re ( z 1 ​ ) = r cos θ , lm ( Z ˉ 1 ​ ) = − r sin θ ⇒ − c o s θ s i n θ ​ = 1 − 2 ​ ⇒ tan θ = 2 ​ − 1 ⇒ θ = 8 π ​ If the number of sides be n , then θ = n π ​ ⇒ n = 8

Mathematics - Complex Number Question with Solution | TestHub

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