Question

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!!

Answer 1

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)

Answer 2

To the person who solved this, you forgot the importance of the I and to include it in your answer