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If |z|=2 then -1+5z lie on 1).circle 2).parabola . 3).hyperbola

If |z|=2 then -1+5z lie on 1).circle 2).parabola . 3).hyperbola

Grade:12

2 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
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mycroft holmes
272 Points
7 years ago
z’ = 1+5z and so z’+1 = 5z which means |z’+1| = 5|z| = 10 which means z’ lies on a circle centred at (-1,0) and radius 10.
 
Alternatively you can see that 5z takes all points on the circle |z| =2 to the circle |z|=10 (it expands the circle). Then 5z -1 is simply displacing the circle left by 1 unit...so the figure remains a circle. This has the advantage of noticing that the whole process is reversible – you can map points on both circles bijectively to each other

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