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signIm -- the sign of the imaginary part of a complex number

Introduction

signIm(z) represents the sign of Im(z).

Call(s)

signIm(z)

Parameters

z - an arithmetical expression representing a complex number

Returns

either +/- 1, 0, or a symbolic call.

Overloadable:

z

Details

Example 1

For numerical values, the position in the complex plane can always be determined:

>> signIm(2 + I), signIm(- 4 - I*PI), signIm(0.3), signIm(-2/7),
   signIm(-sqrt(2) + 3*I*PI)
                              1, -1, -1, 1, 1

Symbolic arguments without properties lead to unevaluated calls:

>> signIm(x), signIm(x - I*sqrt(2))
                                                1/2
                       signIm(x), signIm(x - I 2   )

Properties set via assume are taken into account:

>> assume(x, Type::Real): signIm(x - I*sqrt(2))
                                    -1
>> assume(x > 0): signIm(x)
                                    -1
>> assume(x < 0): signIm(x)
                                     1
>> assume(x = 0): signIm(x)
                                     0
>> unassume(x):

Example 2

signIm is a constant function, apart from the jump discontinuities along the real axis. These discontinuities are ignored by diff:

>> diff(signIm(z), z)
                                     0

Also series treats signIm as a constant function:

>> series(signIm(z/(1 - z)), z = 0)
                               /    z    \      6
                         signIm| ------- | + O(z )
                               \ - z + 1 /

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