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Question

$$z_{1}$$ and $$z_{2}$$ be two complex numbers with a and $$\mathrm{b}$$ as their principal arguments, such that $$\mathrm{a}+\mathrm{b}>\pi$$, then principal $$\mathrm{A}\mathrm{r}\mathrm{g} (z_{1}z_{2})$$ is


A
α+β+π
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B
α+βπ
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C
α+β2π
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D
α+β
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Solution

The correct option is B $$\alpha+\beta-2\pi$$
$$arg z_{1}=a$$
$$arg z_{2}=b$$
$$a+b>\pi $$
$$arg\left ( z_{1}z_{2} \right )=argz_{1}+argz_{2} =a+b$$
Here, $$(a+b)$$ is one of the arguments but not the principle argument because principle argument E$$\left ( -\pi ,\pi  \right )$$
$$\therefore$$ Principle argument $$=a+b-2\pi $$

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