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complex numbers question

the square root of -1 is i, right? Are we assuming the square root is positive? :redface: how can we just assume that though lol. why is it not -i? xx :smile:
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mqb2766
21
Original post by Qxi.xli
the square root of -1 is i, right? Are we assuming the square root is positive? :redface: how can we just assume that though lol. why is it not -i? xx :smile:

Principal root, rather than positive. -i is the other square root.
Original post by mqb2766
Principal root, rather than positive. -i is the other square root.

im sorry, wdum? Principal root according to google (i just searched it up lol) means the positive root? xx:smile:
(edited 3 years ago)
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mqb2766
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Original post by Qxi.xli
im sorry, wdum? Principal root according to google (i just searched it up lol) means the positive root? xx:smile:

It doesn't make much sense to talk about the positive root, when the root is complex. You usually write it in polar/exponential notation and the argument, in this case, would be
pi/2 +k*pi
Where k=1,2. It comes from the usual multiple angles.
Original post by mqb2766
It doesn't make much sense to talk about the positive root, when the root is complex. You usually write it in polar/exponential notation and the argument, in this case, would be
pi/2 +k*pi
Where k=1,2. It comes from the usual multiple angles.

ahah kk i just wont question it lol

so just to clarify then, the square root of -1 is only i?
Reply 5
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mqb2766
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Original post by Qxi.xli
ahah kk i just wont question it lol

so just to clarify then, the square root of -1 is only i?

No, i and -i are both square roots of -1.
There are 3 cube roots of 1 or -1, ...
Is it not covered in your textbook, nth complex roots of unity?
Original post by mqb2766
No, i and -i are both square roots of -1.
There are 3 cube roots of 1 or -1, ...
Is it not covered in your textbook, nth complex roots of unity?

nope ive never ever heard of it lol
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mqb2766
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https://tutorial.math.lamar.edu/Extras/ComplexPrimer/Roots.aspx
https://www.furthermathstutor.co.uk/fp2/complex-numbers.html
Many others ...
(edited 3 years ago)
Original post by mqb2766

kk thank you :smile: it isnt covered in our spec i think, so im just going to remember for a levels that root -1 means i, haha. :smile:
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mqb2766
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Original post by Qxi.xli
kk thank you :smile: it isnt covered in our spec i think, so im just going to remember for a levels that root -1 means i, haha. :smile:

Sounds good.
Reply 10
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davros
16
Original post by Qxi.xli
ahah kk i just wont question it lol

so just to clarify then, the square root of -1 is only i?

All numbers apart from 0 have two square roots. If you label one of the square roots as i, then (-i)^2 = (-1 x i)^2 = (-1)^2 x i^2 = 1 x -1 = -1 so -i is also a square root of -1. But you can't call one of them "positive" and the other "negative" - complex numbers don't have an ordering, unlike real numbers. You can't say 4 + 3i > 2 - 6i for example - it doesn't make sense :smile:
Original post by davros
All numbers apart from 0 have two square roots. If you label one of the square roots as i, then (-i)^2 = (-1 x i)^2 = (-1)^2 x i^2 = 1 x -1 = -1 so -i is also a square root of -1. But you can't call one of them "positive" and the other "negative" - complex numbers don't have an ordering, unlike real numbers. You can't say 4 + 3i > 2 - 6i for example - it doesn't make sense :smile:

thank you! <3

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