First slide

Algebra of complex numbers

Question

If |z - 3| = min {|z - 1|, |z - 5|}, then Re(z) equals to

Moderate

A

2
B

$\frac{5}{2}$
C

$\frac{7}{2}$
D

4

Solution

If |z - 3| = |z - 1|, then z lies on perpendicular bisector of line segment joining ‘1’ and ‘3’. So, Re(z) = 2.
If |z - 3| = |z - 5|, then z lies on perpendicular bisector of line segment joining '3' and '4'. So, Re(z) = 4.

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