Answer:
[tex]z=2(-\sqrt{3}+i)[/tex]
Step-by-step explanation:
The given polar representation of the complex number is:
[tex]z=4(cos(150)^{\circ}+isin(150)^{\circ})[/tex]
Thus, by solving the above equation, we have
⇒[tex]z=4(cos(90+60)+isin(90+60))[/tex]
⇒[tex]z=4(-sin60^{\cic}+icos60^{\circ})[/tex]
⇒[tex]z=4(\frac{\sqrt{3}}{2}+i\frac{1}{2}[/tex]
⇒[tex]z=2(-\sqrt{3}+i)[/tex]
which is the required rectangular form of the given polar complex number.
