Since 210=180+30, we have
[tex]\cos(210)=-\cos(30)=-\dfrac{\sqrt{3}}{2}[/tex]
[tex]\cos(210)=-\sin(30)=-\dfrac{1}{2}[/tex]
So, we have
[tex]z=2\left(-\dfrac{\sqrt{3}}{2} - \dfrac{i}{2}\right) = -\sqrt{3}-i[/tex]
The polar form of the complex number to its equivalent rectangular form will be z= -√3-i.
A complex number is one that has both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.
The given polar form of the complex number as;
z = 2(cos 210° + i sin 210°)
Cos 210° is written as,
[tex]\rm cos \ 210^ 0 = - cos 30^0 = - \frac{\sqrt 3}{2}[/tex]
Cos 210° is also written as,
[tex]\rm cos \ 210^ 0 = - sin \ 30^0 = - \frac{1}{2}[/tex]
The rectangular form of the complex number is obtained by substituting the value as ;
[tex]\rm z = 2(-\frac{\sqrt 3}{2} -\frac{i}{2} ) \\\\ z = - \sqrt 3 -i[/tex]
Hence, the polar form of the complex number to its equivalent rectangular form will be z= -√3-i.
To learn more about the complex number, refer to the link;
https://brainly.com/question/10251853
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