First slide

Geometry of complex numbers

Question

System of equations |z + 3| - |z - 3| = 6 and |z - 4| = r, where $r \in R^{+}$ has

Moderate

A

one solution if r > 1
B

one solution if r < 1
C

two solutions if r = 1
D

at least one solution

Solution

Equation |z + 3| - |z - 3| = 6 represents a ray to the right of complex number '3'.
|z - 4| = r represents a circle whose center is 4 and radius r.
when radius of circle r = 1, it cuts ray at two points '3' and '5'.
For radius r < 1, circle cuts ray at two points.
when radius of circle r > 1, it cuts ray at only one point.

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