First slide

Algebra of complex numbers

Question

If z₁, z₂and z₃, z₄are two pairs of conjugate complex numbers, then $\arg (\frac{z_{1}}{z_{4}}) + \arg (\frac{z_{2}}{z_{3}})$ equal

Moderate

A

$0, π$
B

$π, - π$
C

$\frac{π}{2}, \frac{3 π}{2}$
D

$0, 2 π$

Solution

$\arg (\frac{z_{1}}{z_{4}}) + \arg (\frac{z_{2}}{z_{3}})$
$= \arg (\frac{z_{1} z_{2}}{z_{4} z_{3}}) + 2 k π = \arg (\frac{{|z_{1}|}^{2}}{{|z_{3}|}^{2}}) + 2 k π = 2 k π$
where k = 0 or 1
[ $z_{1} = z_{3} = i,$ gives answer 2p and $z_{1} = z_{3} = 1$ , gives answer 0]

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