Asked by Ellie
                Convert the rectangular coordinate                     (-8,i (square root of 3) into polar coordinates. 
How do I do this?? I tried every way I knew of to convert the y coordinate (i (square root of three)) to polar form, but it didn't work. I think that the polar form of the x coordinate is square root of 61. Thank you!!
            
            
        How do I do this?? I tried every way I knew of to convert the y coordinate (i (square root of three)) to polar form, but it didn't work. I think that the polar form of the x coordinate is square root of 61. Thank you!!
Answers
                    Answered by
            Steve
            
    Think of the unit circle (or any circle centered at (0,0) for that matter). At any angle θ,
tanθ = y/x
r^2 = x^2+y^2
Complex number a+bi is plotted in the x-y plane, so
r^2 = 8^2+√3^2 = 64+3
r = √67
tanθ = √3/-8
That is in QIV (where x is positive and y is negative), so
θ = -12.22° or 0.213 radians
In polar coordinates, that is, of course,
(√67, -0.213)
    
tanθ = y/x
r^2 = x^2+y^2
Complex number a+bi is plotted in the x-y plane, so
r^2 = 8^2+√3^2 = 64+3
r = √67
tanθ = √3/-8
That is in QIV (where x is positive and y is negative), so
θ = -12.22° or 0.213 radians
In polar coordinates, that is, of course,
(√67, -0.213)
                    Answered by
            corrector
            
    To the person who solved this, you forgot the importance of the I and to include it in your answer
    
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