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Why does |i|=1?

Can anyone explain to me why

|i|=1

? I understand that

|x|=x

x>0

and

|x|=-x

x<0

, but

i

is neither positive or negative, so how can we find the absolute value of it?

Reply 1

Omghacklol

Original post by A Confused Guy

Can anyone explain to me why

|i|=1

? I understand that

|x|=x

x>0

and

|x|=-x

x<0

, but

i

is neither positive or negative, so how can we find the absolute value of it?

The modulus function,

|x|=x

x>0

and

|x|=-x

x<0

, is correct as you defined it when x is a real number. It is defined differently for complex numbers: namely, for the complex number a+bi, it is defined as

\sqrt{a^2+b^2}

(the distance between it and the origin on the Argand diagram. So from this, clearly |i|=1

Reply 2

rayquaza17

|a+bi|=\sqrt{a^2+b^2}

|i|=|0+1i|=\sqrt{1^2}=1

Like omghacklol says, what you have wrote is only valid for real numbers. :smile:

(edited 8 years ago)

Reply 3

username1138850

The other two answers may be considered slightly more "mathematical" but if you consider the modulus function simply to find the magnitude of a value, then you know the value of i = root(-1) but since we're just looking at the magnitude, or amount, then this is equal to root(1) which is just 1.

Reply 4

Smaug123

Original post by A Confused Guy

Can anyone explain to me why

|i|=1

? I understand that

|x|=x

x>0

and

|x|=-x

x<0

, but

i

is neither positive or negative, so how can we find the absolute value of it?

The notion generalises massively. Don't expect to understand the following, but you might possibly have seen some of the words before. I'm just giving it to show that the absolute value is not an arbitrary choice of definition; it is the reason why