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Quick one. How do you rotate a sine wave on the complex plane? I already rotated the point $0+i$ to get the unit circle and graphed $n,e^{i \pi n}$ to get a sine wave, which is what all the examples are about. I now want to rotate the result at a $45^\circ$ angle. How do you do that?

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You can rotate the complex plane 45 degrees counterclockwise (and any graph within it at the same time) by multiplying each point by $\frac{1+i}{\sqrt{2}}$.

You should be aware that, depending on your rotation, it may not be a graph of the real component of the complex number anymore, though.

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  • $\begingroup$ Yeah, I used the input as the real part of the complex number to get a wave from the circle and just multiplied that number by $1+i$. Thanks. $\endgroup$ – dataphile Apr 13 '20 at 13:02
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    $\begingroup$ Ok, but the you should be aware that your graph has been scaled as well as rotated. $\endgroup$ – rschwieb Apr 13 '20 at 13:02
  • $\begingroup$ oh I see that now. Is that what the $\sqrt{2}$ is for, to correct that? $\endgroup$ – dataphile Apr 13 '20 at 13:12
  • $\begingroup$ @dataphile Yes. ${}{}{}{}{}{}{}$ $\endgroup$ – rschwieb Apr 13 '20 at 13:12
  • $\begingroup$ Ok, cool, thanks $\endgroup$ – dataphile Apr 13 '20 at 13:13

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