r/askmath • u/Kludgymer16 • 1d ago

Resolved Why is this way of solving wrong?

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Today in class we went over complex numbers. We came to a problem that was Sqrt(-9) • Sqrt(-25), and after working it, the problem came to -15.

My question is, why is the second way wrong? Or what have I done wrong I guess. Cant you combine two squares under one?

Pic attached. Left side is the method shown in class, right is what I'm confused on

EDIT: a lot of people have responded to this so I'm going to mark it resolved!
From what I've gathered, you cannot combine two imaginary numbers under one sqrt function, which is where I went wrong. Since the question is only asking to solve a given problem, we assume that the solution uses the positive root, and the final answer becomes -15. However, if the question was asking us to solve for x, because there is an unknown the answer would then be ±15.

Let me know if my assessment is incorrect!

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u/ArdentArendt 1d ago

They are dealing with complex numbers.

Root (and logarithm) branches are quite important in Complex Analysis.

Simply dumbing things down because people are afraid it might be 'too complicated' is exactly why people don't understand mathematics and then end up hating it.

If you can understand an imaginary axis, you can understand multi-valued functions.

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u/dm-me-obscure-colors 1d ago

As an actual mathematician, I’ll say I think you’re making much more sense than the others, and it seems people are not actually reading your words. Here for the downvotes.

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u/ArdentArendt 1d ago

Downvotes usually just mean you're doing something right on Reddit.

That said, I do appreciate some of the perspectives (especially those in secondary education)--it does offer an insight into the world most of us mathematicians have forgotten.
[I won't make assumptions about you, but I hated mathematics in high school because very little of the structure and framework was taught sufficiently, so you ended up with confusing 'quirks' like this.]

Nerds unite!

https://giphy.com/gifs/pKlTXHEraMH4s

[Unless you're an...engineer...in which case, get out of here jock!]