Answer:
z = (-√3 + i)
Step-by-step explanation:
We have to write [tex]z=2[cos(\frac{5\pi }{6})+isin(\frac{5\pi }{6})][/tex] in the rectangular form.
We will simplify this equation
[tex]z=2[cos(\frac{5\pi }{6})+isin(\frac{5\pi }{6})][/tex]
Since [tex]cos(\frac{5\pi }{6})=-\frac{\sqrt{3} }{2}[/tex]
and [tex]sin(\frac{5\pi }{6})=\frac{1}{2}[/tex]
Now we put the values in the equation
[tex]z=2[-\frac{\sqrt{3} }{2} +i(\frac{1}{2}) ][/tex]
z = (-√3 + i)
Therefore the answer is z = -√3 + i
