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Properties of Argument

If π3 and π4 ...

Question

If $\frac{π}{3}$ and $\frac{π}{4}$ are arguments of $z_{1}$ and ${¯ ¯ ¯ z}_{2}$ , then the value of $arg (z_{1} z_{2})$ is

A

\frac{5 π}{12}

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B

\frac{π}{12}

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C

\frac{7 π}{12}

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D

- \frac{π}{12}

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Solution

The correct option is B $\frac{π}{12}$
$arg (_{2}) = \frac{π}{4}$
$\Rightarrow arg (z_{2}) = - arg (_{2}) = - \frac{π}{4}$
$∴ arg (z_{1} z_{2}) = \frac{π}{3} + (- \frac{π}{4}) = \frac{π}{12}$

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