A $135^\circ$ rotation around the origin in the counter-clockwise direction is applied to $\sqrt{2} - 5 \sqrt{2} i.$  What is the resulting complex number?
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A $135^\circ$ rotation around the origin in the counter-clockwise direction is applied to $\sqrt{2} - 5 \sqrt{2} i.$  What is the resulting complex number?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
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user
4 + 6i
A $135^\circ$ rotation around the origin in the counter-clockwise direction is applied to $\sqrt{2} - 5 \sqrt{2} i.$  What is the resulting complex number?
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