JEE Main 2014 · 11 Apr · Shift 1 · Mathematics Q62

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MathematicsSingle correct+4 / -1Question 62 of 90

If $z_1$ , $z_2$ and $z_3$ , $z_4$ are 2 pairs of complex conjugate numbers, then $\arg\left(\dfrac{z_1}{z_4}\right)+\arg\left(\dfrac{z_2}{z_3}\right)$ equals :

\dfrac\pi2

\dfrac{3\pi}2

\pi

Answer and worked solution

Official answer: A

With $z_2=\bar z_1$ and $z_4=\bar z_3$ :
$\arg\frac{z_1}{z_4}+\arg\frac{z_2}{z_3}=\arg\frac{z_1\bar z_1}{\bar z_3z_3}=\arg\frac{|z_1|^2}{|z_3|^2}=0.$

Topics:Modulus and argument

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JEE Main 2014 · 11 Apr · Shift 1, Mathematics question 62