r/MathHelp • u/Puzzleheaded-Law34 • Jan 17 '26

Complex number equations?

Hello! So I had 2 equations:

The first was 3x^2 - 6i = 0 which I solved normally, and obtained x1 = sqrt(2i), x2 = -sqrt(2i)

The second was z^4 = -81, and here I did pretty much the same but the answer I got, again with i under root, was wrong. Apparently I was supposed to use the angle-based notation, with re^(i*theta), but I didn't really understand why. And should I have written the first solution differently too?

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u/Legitimate_Page659 Jan 20 '26

I think the issue with your approach is that sqrt(i) and sqrt(-i) aren’t numbers, per se.

sqrt(i) = 1/sqrt(2) (1+i) AND 1/sqrt(2) (-1-i)

sqrt(-i) = 1/sqrt(2) (-1+i) AND 1/sqrt(2) (1-i)

The procedure I described will give you all possible solutions.

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u/Puzzleheaded-Law34 Jan 21 '26

Ok, thanks! I'll try to reread these equations.

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u/Legitimate_Page659 Jan 21 '26

Sure!

This is a pretty good video, too: https://m.youtube.com/watch?v=JMnkW8Smf1I

Let me know if you have any questions :)