First slide

Algebra of complex numbers

Question

If $z$ is a non-zero complex number, then arg $(z) + a r g (z)$ equals

Moderate

A

0
B

$π$
C

$2 π$
D

none of these

Solution

If $z \in R$ and $z < 0$ then
$\begin{array}{l} \arg (z) = \arg (\bar{z}) = π \\ \Rightarrow \arg (z) + \arg (\bar{z}) = 2 π \end{array}$
Suppose $z \in C, z \neq 0$ and $z$ is not a negative real number.
Let t $a r g (z) = a,$ where $- π < α < π$
In this case $\arg (\bar{z}) = - α$ , so that
$\arg (z) + \arg (z) = 0$

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