$\frac{4 \operatorname{cis}\left(152^{\circ}\right)}{3 \operatorname{cis}\left(108^{\circ}\right)}$
Answer
Final Answer: \(\boxed{\frac{4}{3} \operatorname{cis}(44^\circ)}\)
Step 1 ：The problem is asking to divide two complex numbers in polar form. The polar form of a complex number is \(r(\cos(\theta) + i\sin(\theta))\), which can also be written as \(r \operatorname{cis}(\theta)\).
Step 2 ：When dividing two complex numbers in polar form, we divide the magnitudes and subtract the angles.
Step 3 ：So, we need to divide 4 by 3 and subtract 108 degrees from 152 degrees.
Step 4 ：Calculate the magnitude: \(\frac{4}{3} = 1.3333333333333333\)
Step 5 ：Calculate the angle: \(152^\circ - 108^\circ = 44^\circ\)
Step 6 ：Final Answer: \(\boxed{\frac{4}{3} \operatorname{cis}(44^\circ)}\)
