Let $z = -1 - \sqrt{3}i$. State the value of $|-1 - \sqrt{3}i|$ and \(\arg(-1 - \sqrt{3}i)\

Question

Let $z = -1 - \sqrt{3}i$. State the value of $|-1 - \sqrt{3}i|$ and $\arg(-1 - \sqrt{3}i)$. Give the geometrical meanings of the statements "$|-1 - \sqrt{3}i|$" and "$\arg(-1 - \sqrt{3}i)$".

Accepted Answer

(i) $|z|=2$, $\arg z=-\dfrac{2\pi}{3}$ (ii) $|z|$ is the distance $OP$, and $\arg z$ is the directed angle from the positive real axis to $OP$

Complex Numbers - Modulus and Argument of Complex Numbers

Complex Numbers - Modulus and Argument of Complex Numbers

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