Let $\mathcal{z}_{1}$ and$\ \mathcal{z}_{2}$ be two complex numbers with $\alpha$ and $\beta$ as their principle arguments such that $\alpha + \beta \pi,$ then principal $\arg{(\mathcal{z}_{1}\mathcal{z}_{2})}\$is given by

Question

Let $\mathcal{z}_{1}$ and$\ \mathcal{z}_{2}$ be two complex numbers with $\alpha$ and $\beta$ as their principle arguments such that $\alpha + \beta > \pi,$ then principal $\arg{(\mathcal{z}_{1}\mathcal{z}_{2})}\$is given by

Dr. Abubacker · Accepted Answer

(b)
We know that principle argument of a complex number lie between $–\pi\ and\ \pi,\ but\ \alpha + \beta > \pi$
Therefore, principle
$\arg(\mathcal{z}_{1}\mathcal{z}_{2}) = \arg{\left( \mathcal{z}_{1} \right) + \arg{\left( \mathcal{z}_{2} \right) = \alpha + \beta\ }\ }$is give by $\alpha + \beta - \pi$

Q. Let $\mathcal{z}_{1}$ and$\ \mathcal{z}_{2}$ be two complex numbers with $\alpha$ and $\beta$ as their principle arguments such that $\alpha + \beta > \pi,$ then principal $\arg{(\mathcal{z}_{1}\mathcal{z}_{2})}\$is given by

Explanation

Reviewed by Dr. Abubacker

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