Question

Find the modulus and amplitude of $-\sqrt{3}-i$

• A. $|z|=2;amp\left(z\right)=-\frac{5\pi }{6}$
• B. $|z|=4;amp\left(z\right)=\frac{5\pi }{6}$
• C. $|z|=4;amp\left(z\right)=-\frac{\pi }{6}$
• D. none of these

Answer 1

The correct option is A $|z|=2;amp\left(z\right)=-\frac{5\pi }{6}$

$z=-\sqrt{3}-i$ $|z|=2$

$=2\left(\frac{-\sqrt{3}-i}{2}\right)$

$=2e^{i(\frac{\pi }{6}-\pi )}$

$=2e^{i\frac{-5\pi }{6}}$

$=|z|.e^{iarg\left(z\right)}$

Hence

$|z|=2$ and $arg\left(z\right)=\frac{-5\pi }{6}$.