Question

Convert 4(cos(120)+i sin(120)) into rectangular form

Answer 1

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 2

Answer:

Option B $(-2,2\sqrt{3})$                

Step-by-step explanation:

Given : Expression $4(\cos(120)+i \sin(120))$

To find : Convert the expression into rectangular form?

Solution :    

The rectangular form is $a+ib$

Now, We solve the expression

$4(\cos(120)+i \sin(120))$

$=4(\cos(90+30)+i \sin(90+30))$

Applying trigonometric properties,

$\cos(90+\theta)=-\sin\theta\\\sin(90+\theta)=\cos\theta$

$=4(-\sin(30)+i \cos(30))$

Substitute, $\sin(30)=\frac{1}{2}\ , \cos\tehta (30)=\frac{\sqrt{3}}{2}$

$=4(-\frac{1}{2}+i\frac{\sqrt{3}}{2})$

$=-4\times \frac{1}{2}+4\times \frac{\sqrt{3}}{2})i$

$=-2+2\sqrt{3}i$

Therefore, The rectangular form is $4(\cos(120)+i\sin(120))=-2+2\sqrt{3}i$

So, Option B is correct $(-2,2\sqrt{3})$