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March 3rd, 2014, 08:09 PM   #1
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i am imaginary


Is i < or > or = 1?

1) Since i is not on the real number line this question is meaningless

ON THE OTHER HAND

2) Since and -1 < 1 it follows that i < 1

What is the right answer?
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March 4th, 2014, 11:54 AM   #2
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If i is not a real number, none of the choices mentioned in the question applies.

The second suggestion is incorrect, as what would follow is i < 1, which doesn't imply i < 1.
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March 4th, 2014, 12:06 PM   #3
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Re: i am imaginary

Quote:
Originally Posted by shunya

Is i < or > or = 1?

1) Since i is not on the real number line this question is meaningless

ON THE OTHER HAND

2) Since and -1 < 1 it follows that i < 1
What is the right answer?
i cannot be negative because negative times negative number is positive number.
i cannot be positive because positive number times positive number is positive number.

i is neither negative nor positive.


But what are +i and -i ?
Is +i positive and -i negative?
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March 4th, 2014, 01:03 PM   #4
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Both +i (which equals i) and -i are imaginary, not real. Hence neither should be called positive or negative.

However, the imaginary part of +i is 1 (which is positive) and the imaginary part of -i is -1 (which is negative).
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March 4th, 2014, 01:29 PM   #5
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Re: i am imaginary

How is this possible?
Does i have two values:




Because
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March 5th, 2014, 01:49 AM   #6
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No, just as 3 = (-3) = 9 doesn't mean that 3 has two values. Like any non-zero number, -1 has two square roots, i and -i. A positive real has one positive and one negative square root. Any other non-zero number has one square root with a positive imaginary part and one square root with a negative imaginary part.
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March 5th, 2014, 02:30 AM   #7
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Re:

Quote:
Originally Posted by skipjack
No, just as doesn't mean that 3 has two values. Like any non-zero number, -1 has two square roots, i and -i.
If we write , why this could not be understood that
3 has two values +3 and -3. Isn't it only a general agreement that 3=+3 ? Why we could not instead use a convention
that 3=-3 ?

If -1 has two square roots, i and -i


it is the same as


meaning that i has two values: +i and -i, which we can plot on the complex plane on the opposite sides
of unit circle.

Last edited by TwoTwo; March 28th, 2014 at 11:33 PM.
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March 5th, 2014, 03:14 AM   #8
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With such a convention, adding 3 = 3 to 3 = -3 would give 6 = 0, etc., which doesn't seem useful. In the case of +i and -i, you have acknowledged these correspond to opposite sides of a unit circle, and this wording acknowledges that the opposite sides are not the same side, so it would be confusing to hold that +i and -i are the same or equal.
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