SOLUTION: Please help. I do not understand Write the complex number in rectangular form. 1.) 3(cos*pi/3 + sin*pi/3) ----------- ----------- ----------- ----------- ----------- ----- wr

1.) 

Just evaluate it:

    

    




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3√3 - 3i = x + iy,

where  P(x,y) =  P(3√3,-3),

Plot the point P(x,y) = P(3√3,-3),
draw a line from P to the origin, 
and another line from P perpendicular to the x-axis.  
Label the sides of the resulting right triangle x,y, and r,
Label the counter-clockwise angle q.




Since the point P is P(x,y) =  P(3√3,-3), x = 3√3 and y = -3.

We calculate r:

r² = x² + y²
r² = (3√3)² + (-3)².
r² = 9(3) + 9
r² = 27 + 9
r² = 36
 r = √36
 r = 6



Therefore q = 330°,

since it is in Q4, with a reference angle of 30°.

    Use  and .
Solve them for x and y

     and 

    x = 6*cos(330°) and y = 6*sin(330°)

So
 
3√3 - 3i = x + iy =  6*cos(330°) + i*6sin(330°) = 6(cos(330° + isin(330°)  

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convert the polar equation to rectangular form.
3.) r = 5

That is a circle at the origin (pole) with a radius of 5.

r² = x² + y²
5² = x² + y²
x² + y² = 25

Edwin