Question

Please help I’ll give brainliest

Answer 1

Answer:

  $\dfrac{z_1}{z_2}=\dfrac{1}{2}\,\text{cis}\,\dfrac{7\pi}{12}$

Step-by-step explanation:

The quotient of complex numbers is the quotient of their magnitudes at the difference of their angles.

  $\dfrac{z_1}{z_2}=\dfrac{\text{cis}\,\dfrac{2\pi}{3}}{2\,\text{cis}\,\dfrac{\pi}{12}}=\dfrac{1}{2}\,\text{cis}\left(\dfrac{2\pi}{3}-\dfrac{\pi}{12}\right)\\\\\bf{\dfrac{z_1}{z_2}=\dfrac{1}{2}\,\text{cis}\,\dfrac{7\pi}{12}}$