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 October 26th, 2017, 05:07 AM #1 Senior Member   Joined: Nov 2011 Posts: 116 Thanks: 1 complex number and "minus" number Can I "define" -3 as minus one x 3 like 3i as 3 x root of (-1)?
October 26th, 2017, 05:44 AM   #2
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Quote:
 Originally Posted by shaharhada Can I "define" -3 as minus one x 3 like 3i as 3 x root of (-1)?
$\displaystyle -3 = (-1)3 = \frac{3}{-1}$

All of these are valid.

-Dan

October 27th, 2017, 08:27 AM   #3
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Quote:
 Originally Posted by shaharhada Can I "define" -3 as minus one x 3 like 3i as 3 x root of (-1)?
If I understand your question, then the answer is no.

$-\ 3 = 3(- 1) \ne 3i.$

The reason is that:

$i = -\ 1 \implies i^2 = 1 \text {, but } i^2= -\ 1 \ne 1 \text { by the definition of } i.$

October 27th, 2017, 08:38 AM   #4
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Quote:
 Originally Posted by shaharhada Can I "define" -3 as minus one x 3 . . .
How are you defining "minus one"?

 October 27th, 2017, 11:09 AM #5 Math Team     Joined: May 2013 From: The Astral plane Posts: 1,659 Thanks: 652 Math Focus: Wibbly wobbly timey-wimey stuff. I think the OP was asking if we could write a number as a + (-1)b, similar to the concept a + ib. -Dan
October 27th, 2017, 12:27 PM   #6
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Quote:
 Originally Posted by topsquark I think the OP was asking if we could write a number as a + (-1)b, similar to the concept a + ib. -Dan
But a + ib includes negative a and negative b

October 27th, 2017, 05:39 PM   #7
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Quote:
 Originally Posted by studiot But a + ib includes negative a and negative b
I agree, but you can put any (real) expression into an a + (-1)b format. I'm not arguing the OP's reasoning for doing it, just what I think the OPs question is referring to.

-Dan

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