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Geometrical Representation of Argument and Modulus

If z is pur...

Question

If $z$ is purely real and $R e (z) < 0$ , then $a r g (x)$ is

0

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π

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- π

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\frac{π}{2}

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Solution

The correct option is B $π$
Given $z$ is purely real is $z = a + i (0)$ for some $a \in R$

$\Rightarrow z = a$

given $R e (z) < 0$

$\Rightarrow a < 0$

$∴ z$ can be represented as Ref. image

$∴ A r g (z) = π$

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