# Rotate sine wave on complex plane

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?

You can rotate the complex plane 45 degrees counterclockwise (and any graph within it at the same time) by multiplying each point by $$\frac{1+i}{\sqrt{2}}$$.
• 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. – dataphile Apr 13 '20 at 13:02
• oh I see that now. Is that what the $\sqrt{2}$ is for, to correct that? – dataphile Apr 13 '20 at 13:12
• @dataphile Yes. ${}{}{}{}{}{}{}$ – rschwieb Apr 13 '20 at 13:12