Question 1182669
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The angles aren't being rotated; the vectors are.<br>
For the complex number a+bi, the reference angle is {{{tan^(-1)(b/a)}}}; then to get the actual angle you need to consider which quadrant the vector is in.<br>
For the complex number -5-5i, the reference angle is arctan(-5/-5) = arctan(1), which is 45 degrees.  With both components negative, the vector is in quadrant III, so the angle is 180+45 = 225 degrees.<br>
The complex number 3+4i is in quadrant I, so the angle for 3+4i is {{{tan^(-1)(4/3)}}}<br>
Find that angle; I'll call it x (degrees).  To rotate the vector at 225 degrees to coincide with the vector at x degrees, you will "pass 0 degrees".  So the calculation to find the angle through which the first vector is rotated to coincide with the second is (x+360)-225.<br>
I leave the actual calculations to you.<br>
Note that the first vector has a reference angle of 45 degrees in quadrant III and the second has a reference angle greater than 45 degrees in quadrant I, so the answer you come up with should be something slightly more than 180 degrees.<br>