The principal argument of $z = - 3 + 3 i$ is:

\frac{π}{4}

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- \frac{π}{4}

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\frac{3 π}{4}

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- \frac{3 π}{4}

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Solution

The correct option is C $\frac{3 π}{4}$
Given, $z = - 3 + 3 i$

$\Rightarrow z = 3 (- 1 + i)$

$= 3 (\frac{- 1}{\sqrt{2}} + \frac{i}{\sqrt{2}})$

$= 3 \sqrt{2} (cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4}))$

$= 3 \sqrt{2} e^{i \frac{3 π}{4}}$

Hence, principal argument of $z$ is $\frac{3 π}{4}$ .

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