First slide

Geometry of complex numbers

Question

If $z = 5 + t + i \sqrt{25 - t^{2}}, (- 5 \leq t \leq 5)$ then locus of z is a curve which passes through

Moderate

A

$5 + 0 i$
B

$- 2 + 3 i$
C

$2 + 4 i$
D

$- 2 - 3 i$

Solution

Let $z = x + i y$ so that
$x = 5 + t, y = \sqrt{25 - t^{2}}$
$\Rightarrow (x - 5)^{2} + y^{2} = 25$
This clearly passes through $2 + 4 i$

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