So this is the problem as written and I'm totally lost. Any help or explanation would be greatly appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

"Viewing ℂ=ℝ^{2}, we can identify the complex numbers z = a+bi and w=c+di with the vectors (a,b) and (c,d) in R2 , respectively. Then we can form their dot product, (a,b)[itex]\bullet[/itex](c,d)=ac+bd.

Prove that ζ[itex]\bar{c}[/itex] + c = 0 iff c is orthogonal to [itex]\sqrt{ζ}[/itex]."

I feel like there are too many things undefined - or maybe I just don't get what things are supposed to be. [itex]\bar{c}[/itex] is supposed to be the conjugate of c, I know that much. And in another problem ζ was defined as cosθ + i sinθ, but I'm not sure how to use this information (or if it even applies to this problem). I know that c and ζ being orthogonal means they're both vectors and their dot product is zero. It's in the chapter on isometries of ℝ and ℂ.

I've been trying to figure this problem out for hours and am frustrated to the point of tears. Please help.

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# (Algebra) Isometries on the complex plane

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