2. Express each complex number in the form $\operatorname{cis} \theta$ where $-\pi< \theta \leq \pi$ :
(a) $\operatorname{cis} 5 \pi$
(b) $\operatorname{cis} \frac{-11 \pi}{6}(\mathrm{c})-\operatorname{cis} \frac{\pi}{4}$
(c) \(\boxed{\operatorname{cis} -0.785}\)
Step 1 :Express each complex number in the form \(\operatorname{cis} \theta\) where \(-\pi<\theta \leq \pi\):
Step 2 :(a) \(\operatorname{cis} 5 \pi\)
Step 3 :(b) \(\operatorname{cis} \frac{-11 \pi}{6}\)
Step 4 :(c) \(\operatorname{cis} \frac{-\pi}{4}\)
Step 5 :Find the equivalent angle in the given range for each complex number:
Step 6 :\(\operatorname{cis} 5 \pi\) has an equivalent angle of \(\operatorname{cis} 3.142\)
Step 7 :\(\operatorname{cis} \frac{-11 \pi}{6}\) has an equivalent angle of \(\operatorname{cis} 0.524\)
Step 8 :\(\operatorname{cis} \frac{-\pi}{4}\) has an equivalent angle of \(\operatorname{cis} -0.785\)
Step 9 :\(\boxed{\text{Final Answer:}}\)
Step 10 :(a) \(\boxed{\operatorname{cis} 3.142}\)
Step 11 :(b) \(\boxed{\operatorname{cis} 0.524}\)
Step 12 :(c) \(\boxed{\operatorname{cis} -0.785}\)