# signIm

Sign of the imaginary part of complex number

## Syntax

``signIm(z)``

## Description

example

````signIm(z)` returns the sign of the imaginary part of a complex number `z`. For all complex numbers with a nonzero imaginary part, ```singIm(z) = sign(imag(z))```. For real numbers, ```signIm(z) = -sign(z)```.```

## Examples

### Symbolic Results Including signIm

Results of symbolic computations, especially symbolic integration, can include the `signIm` function.

Integrate this expression. For complex values `a` and `x`, this integral includes `signIm`.

```syms a x f = 1/(a^2 + x^2); F = int(f, x, -Inf, Inf)```
```F = (pi*signIm(1i/a))/a```

### Signs of Imaginary Parts of Numbers

Find the signs of imaginary parts of complex numbers with nonzero imaginary parts and of real numbers.

Use `signIm` to find the signs of imaginary parts of these numbers. For complex numbers with nonzero imaginary parts, `signIm` returns the sign of the imaginary part of the number.

```[signIm(-18 + 3*i), signIm(-18 - 3*i),... signIm(10 + 3*i), signIm(10 - 3*i),... signIm(Inf*i), signIm(-Inf*i)]```
```ans = 1 -1 1 -1 1 -1```

For real positive numbers, `signIm` returns `-1`.

`[signIm(2/3), signIm(1), signIm(100), signIm(Inf)]`
```ans = -1 -1 -1 -1```

For real negative numbers, `signIm` returns `1`.

`[signIm(-2/3), signIm(-1), signIm(-100), signIm(-Inf)]`
```ans = 1 1 1 1```

`signIm(0)` is `0`.

`[signIm(0), signIm(0 + 0*i), signIm(0 - 0*i)]`
```ans = 0 0 0```

### Signs of Imaginary Parts of Symbolic Expressions

Find the signs of imaginary parts of symbolic expressions that represent complex numbers.

Call `signIm` for these symbolic expressions without additional assumptions. Because `signIm` cannot determine if the imaginary part of a symbolic expression is positive, negative, or zero, it returns unresolved symbolic calls.

```syms x y z [signIm(z), signIm(x + y*i), signIm(x - 3*i)]```
```ans = [ signIm(z), signIm(x + y*1i), signIm(x - 3i)]```

Assume that `x`, `y`, and `z` are positive values. Find the signs of imaginary parts of the same symbolic expressions.

```syms x y z positive [signIm(z), signIm(x + y*i), signIm(x - 3*i)]```
```ans = [ -1, 1, -1]```

For further computations, clear the assumptions by recreating the variables using `syms`.

`syms x y z`

Find the first derivative of the `signIm` function. `signIm` is a constant function, except for the jump discontinuities along the real axis. The `diff` function ignores these discontinuities.

```syms z diff(signIm(z), z)```
```ans = 0```

### Signs of Imaginary Parts of Matrix Elements

`singIm` accepts vectors and matrices as its input argument. This lets you find the signs of imaginary parts of several numbers in one function call.

Find the signs of imaginary parts of the real and complex elements of matrix `A`.

```A = sym([(1/2 + i), -25; i*(i + 1), pi/6 - i*pi/2]); signIm(A)```
```ans = [ 1, 1] [ 1, -1]```

## Input Arguments

collapse all

Input representing complex number, specified as a number, symbolic number, symbolic variable, expression, vector, or matrix.

## Tips

• `signIm(NaN)` returns `NaN`.