Answer
$|z|=\displaystyle \frac{2\sqrt{3}}{3}$
see graph below
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Work Step by Step
See p. 602, Graphing Complex Numbers
The complex plane is determined by the real axis and the imaginary axis.
To graph the complex number a + bi, we plot the ordered pair of numbers (a,b) in this plane
See p. 603,
The modulus (or absolute value) of the complex number $z=a+bi$ is
$|z|=\sqrt{a^{2}+b^{2}}$
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$z=-1-\displaystyle \frac{\sqrt{3}}{3}i$
Plot $(a,b)=(-1,-\displaystyle \frac{\sqrt{3}}{3})$ in the complex plane
(see image, $-\displaystyle \frac{\sqrt{3}}{3}\approx -0.577)$
$|z|=\sqrt{(-1)^{2}+(-\frac{\sqrt{3}}{3})^{2}}=\sqrt{1+\frac{1}{3}}$
$=\displaystyle \sqrt{\frac{4}{3}}=\frac{2}{\sqrt{3}}=\frac{2\sqrt{3}}{3}$
