# abs

Symbolic absolute value (complex modulus or magnitude)

## Syntax

``abs(z)``

## Description

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````abs(z)` returns the absolute value (or complex modulus) of `z`. Because symbolic variables are assumed to be complex by default, `abs` returns the complex modulus (magnitude) by default. If `z` is an array, `abs` acts element-wise on each element of `z`.```

## Examples

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`[abs(sym(1/2)), abs(sym(0)), abs(sym(pi) - 4)]`
```ans = [ 1/2, 0, 4 - pi]```

Compute `abs(x)^2` and simplify the result. Because symbolic variables are assumed to be complex by default, the result does not simplify to `x^2`.

```syms x simplify(abs(x)^2)```
```ans = abs(x)^2```

Assume `x` is real, and repeat the calculation. Now, the result is simplified to `x^2`.

```assume(x,'real') simplify(abs(x)^2)```
```ans = x^2```

Remove assumptions on `x` for further calculations. For details, see Use Assumptions on Symbolic Variables.

`assume(x,'clear')`

Compute the absolute values of each element of matrix `A`.

```A = sym([1/2+i -25; i pi/2]); abs(A)```
```ans = [ 5^(1/2)/2, 25] [ 1, pi/2]```

Compute the absolute value of this expression assuming that the value of `x` is negative.

```syms x assume(x < 0) abs(5*x^3)```
```ans = -5*x^3```

For further computations, clear the assumption on `x` by recreating it using `syms`:

`syms x`

## Input Arguments

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Input, specified as a number, vector, matrix, or array, or a symbolic number, vector, matrix, or array, variable, function, or expression.

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### Complex Modulus

The absolute value of a complex number z = x + y*i is the value $|z|=\sqrt{{x}^{2}+{y}^{2}}$. Here, x and y are real numbers. The absolute value of a complex number is also called a complex modulus.

## Tips

• Calling `abs` for a number that is not a symbolic object invokes the MATLAB® `abs` function.