First slide

Algebra of complex numbers

Question

Number of complex numbers such that $| z | = 1$ and $| z = 1 - 2 z$ is

Moderate

A

0
B

1
C

2
D

infinite

Solution

$| z | = 1 \Rightarrow z z = 1$ Therefore $z = 1 - 2 z$
$\Rightarrow z = 1 - \frac{2}{z} \Rightarrow z^{2} - z + 2 = 0$
$\Rightarrow z = \frac{1 \pm \sqrt{7} i}{2}$ but than, $| z | \neq 1$

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