Put /6 - i/12 into polar form?

Sorry, / means square root. My iPhone doesn't have the square root symbol. I've asked this questioned multiple times now, and I know how to do it if my teacher allowed it in decimal form. I would find the radius, which is 3root2, and take the inverse tangent of /12 and /6. BUT. My teacher wants it in exact form, no decimals. This complex number isn't one of the obvious radians, like pie/6 or something. So I'm really confused.

R = √(6+12) = √18 = 3√2,
theta = arctan(-√12 / √6) = -arctan(√2) so
√6 - i√12 = 3√2 * cis( -arctan(√2.

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