First slide

Geometry of complex numbers

Question

The reflection of the complex number $\frac{4 + 3 i}{1 + 2 i}$ in the straight line $i z = \bar{z}$ ,is

Very difficult

A

$1 - 2 i$
B

$4 - 3 i$
C

$3 + 4 i$
D

$2 + i$

Solution

$\frac{(4 + 3 i) (1 - 2 i)}{(1 + 2 i) (1 - 2 i)} = \frac{4 + 3 i - 8 i + 6}{1 + 4} = 2 - i$
$i z = \bar{z}$

$i (x + i y) = x - i y$

$i x - y = x - i y$

$x + y - i (x + y) = 0$

$x + y = 0$

Reflection is $(1 - 2 i)$ .

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