Question
Write each complex number in trigonometric form $r(\cos \theta+i \sin \theta),$ with $\theta$ in the interval$\left[0^{\circ}, 360^{\circ}\right) .$ See Example 3$$\sqrt{3}-i$$
Step 1
The modulus of a complex number $a+bi$ is given by $\sqrt{a^2+b^2}$. In this case, $a=\sqrt{3}$ and $b=-1$. So, we have \[r=\sqrt{(\sqrt{3})^2+(-1)^2}=\sqrt{3+1}=\sqrt{4}=2.\] Show more…
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