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
B
α+βπ
C
α+β2π
D
α+β

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 $$=a+b-2\pi$$Maths

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