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With which complex number can I rotate a vector 60 degrees clockwise?

I do not know where to begin I tried using the unit circle but I keep getting confused. Can someone help me?

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    Are you representing vectors as complex numbers? – 2017-01-24
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    Do you know unitary complex numbers as $e^{i\theta}$? – 2017-01-24
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    Hints: do you know Euler's formula for $e^{it}$? Do you know how to multiply complex numbers when you have expressed them in polar coordinates? – 2017-01-24
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    I know hot to multiply complex numbers, I am trying to understand how you rotate a vector 60 degrees clockwise – 2017-01-24
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    Do you know how to multiply complex numbers *when they are expressed in polar coordinates*? – 2017-01-24
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    $$e^{i\pi\over 3}=\cos{\pi\over 3}+i\sin{\pi\over 3}={1\over 2}+i{\sqrt{3}\over 2}$$ – 2017-01-24
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    the complex number 0,5 + 0.86i is that the answer to rotate the vector? I used the calculator and sin 60 and I got 0.5 which is exactly on the unit circle. I did the same with cos 60 and got 0.86. but to make a 60 degrees rotation i have to use 300 degrees or not? – 2017-01-24

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