Let R denote the set of all real numbers. Let z 1 = 1 + 2 i and z 2 = 3 i be two complex numbers, where i = − 1 . Let S = { ( x , y ) ∈ R × R : ∣ x + i y − z 1 ∣ = 2 ∣ x + i y − z 2 ∣ } . Th

Question

Let R denote the set of all real numbers. Let z 1 ​ = 1 + 2 i and z 2 ​ = 3 i be two complex numbers, where i = − 1 ​ . Let S = { ( x , y ) ∈ R × R : ∣ x + i y − z 1 ​ ∣ = 2 ∣ x + i y − z 2 ​ ∣ } . Then which of the following statements is (are) TRUE?

TestHub · Accepted Answer

​ ​ ∣ x + i y − 1 − 2 i ∣ = 2∣ x + i y − 3 i ∣ ⇒ ( x − 1 ) 2 + ( y − 2 ) 2 = 4 ( x 2 + ( y − 3 ) 2 ) ⇒ 3 x 2 + 3 y 2 + 2 x − 20 y + 31 = 0 ⇒ x 2 + y 2 + 3 2 x ​ − 3 20 y ​ + 3 31 ​ = 0 ​ ∴ S is a circle with centre ( − 3 1 ​ , 3 10 ​ ) and radius = 9 1 ​ + 9 100 ​ − 3 31 ​ ​ = 9 8 ​ ​ = 3 2 2 ​ ​ ​

Mathematics - Complex Number Question with Solution | TestHub

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