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I don't quite fully understand part b and c
 

jimmysmith560

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Would the following working help?





Part (a):

Since



This is a circle with centre the origin and the radius equal to the modulus of w, as follows:

1650797535056.png

Part (b):

This is a circle with centre w and the radius equal to twice the modulus of w, as follows:

1650797619177.png

Part (c):

This is the perpendicular bisector of the line segment through w and the origin, as follows:

1650797669407.png
 

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yanujw

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im still unsure about c
Interpret this as |z-w| = |z-0|, which means the distance from w must be the same as the distance from the point 0. The midpoint of 0 and w (0.5 + 1.5i) is one such point, and it follows that the line perpendicular line passing through this point retains this property.
 

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