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The inequality | z − 6 | < | z − 2 | represents the region given by
- a)Re(z) < 2
- b)Re(z) > 3
- c)Re(z) > 4
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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The inequality| z−6 |<| z−2 | represents the region giv...
The inequality | z | > 5 represents all the complex numbers that have a distance greater than 5 from the origin on the complex plane.
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The inequality| z−6 |<| z−2 | represents the region giv...
Let, z = x + iy
Putting in the given inequality,
∣(x−4) − iy∣ < ∣(x−2) + iy∣
squaring both sides,
⇒ (x−4)2 + y2 < (x−2)2 + y2
⇒ −8x + 16 < −4x + 4
⇒ 4x > 12
⇒ x > 3
⇒ Re(z) > 3
⇒ −8x + 16 < −4x + 4
⇒ 4x > 12
⇒ x > 3
⇒ Re(z) > 3
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The inequality| z−6 |<| z−2 | represents the region given bya)Re(z)<2b)Re(z)> 3c)Re(z)> 4d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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