Is 1+i, Greater than 1?
We don't know, because i is immeasurable.
However the Closest we can get to surmise it's value is, calculating the absolute value of (1+i). Which is 2^(1/2) !
It depends on how you define magnitude, and absolute value/norm is a perfectly valid and rational way to define it.
Not only that, but it actually makes a ton of sense arithmetically. Obviously, norms don't behave the same way as ordinary real numbers in terms of addition, but they behave well under multiplication and related properties such as inversion, i.e. the norm of a product of complex numbers is the product of their norms, the norm of the inverse of an complex number is the inverse of its norm, etc.
We don't know, because i is immeasurable.
However the Closest we can get to surmise it's value is, calculating the absolute value of (1+i). Which is 2^(1/2) !
It depends on how you define magnitude, and absolute value/norm is a perfectly valid and rational way to define it.
Not only that, but it actually makes a ton of sense arithmetically. Obviously, norms don't behave the same way as ordinary real numbers in terms of addition, but they behave well under multiplication and related properties such as inversion, . the norm of a product of complex numbers is the product of their norms, the norm of the inverse of an complex number is the inverse of its norm, etc.
Keep up the Good and Great work @sapphire_kaleidoscope
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We don't know, because i is immeasurable.
However the Closest we can get to surmise it's value is, calculating the absolute value of (1+i). Which is 2^(1/2) !