Respuesta :
Try using polar expression forms. z = r(cos theta + sin theta) as well as x = r cos theta and y = r sin theta. Plug in the values you have. x = 4 cos 120 or 2pi/3 and solve. Do the same for y = 4 sin 120 or 2pi/3. It will give the "x" and "y" parts of your rectangular coordinates.
Answer:
Option B [tex](-2,2\sqrt{3})[/tex]
Step-by-step explanation:
Given : Expression [tex]4(\cos(120)+i \sin(120))[/tex]
To find : Convert the expression into rectangular form?
Solution :
The rectangular form is [tex]a+ib[/tex]
Now, We solve the expression
[tex]4(\cos(120)+i \sin(120))[/tex]
[tex]=4(\cos(90+30)+i \sin(90+30))[/tex]
Applying trigonometric properties,
[tex]\cos(90+\theta)=-\sin\theta\\\sin(90+\theta)=\cos\theta[/tex]
[tex]=4(-\sin(30)+i \cos(30))[/tex]
Substitute, [tex]\sin(30)=\frac{1}{2}\ , \cos\tehta (30)=\frac{\sqrt{3}}{2}[/tex]
[tex]=4(-\frac{1}{2}+i\frac{\sqrt{3}}{2})[/tex]
[tex]=-4\times \frac{1}{2}+4\times \frac{\sqrt{3}}{2})i[/tex]
[tex]=-2+2\sqrt{3}i[/tex]
Therefore, The rectangular form is [tex]4(\cos(120)+i\sin(120))=-2+2\sqrt{3}i[/tex]
So, Option B is correct [tex](-2,2\sqrt{3})[/tex]
