Paragraph: Let A , B , C be three sets of complex numbers as defined below. A = { z ; lm z ≥ 1 } ; B = { z : ∣ z − 2 − i ∣ = 3 } ; C = { z : Re (( 1 − i ) z ) = 2 } . Question: Let z be any point in

Question

Paragraph: Let A , B , C be three sets of complex numbers as defined below. A = { z ; lm z ≥ 1 } ; B = { z : ∣ z − 2 − i ∣ = 3 } ; C = { z : Re (( 1 − i ) z ) = 2 ​ } . Question: Let z be any point in A ∩ B ∩ C and let w be any point satisfying ∣ w − 2 − i ∣ < 3 . Then, ∣ z ∣ − ∣ w ∣ + 3 lies between

TestHub · Accepted Answer

⇒ ⇒ ⇒ ​ ∣ w − ( 2 + i ) ∣ < 3 ∣∣ w ∣ − ∣2 + i ∣∣ < 3 − 3 + 5 ​ < ∣ w ∣ < 3 + 5 ​ − 3 − 5 ​ < − ∣ w ∣ < 3 − 5 ​ ​ Also, ∣ z − ( 2 + i ) ∣ = 3 ⇒ − 3 + 5 ​ − 3 ​ ≤ ∣ z ∣ ≤ 3 + 5 ​ < ∣ z ∣ − ∣ w ∣ + 3 < 9 ​

Mathematics - Complex Number Question with Solution | TestHub

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