# conj

Complex conjugate of quaternion

## Syntax

``quatConjugate = conj(quat)``

## Description

example

````quatConjugate = conj(quat)` returns the complex conjugate of the quaternion, `quat`.If $q=a+b\text{i}+c\text{j}+d\text{k}$, the complex conjugate of q is ${q}^{*}=a-b\text{i}-c\text{j}-d\text{k}$. Considered as a rotation operator, the conjugate performs the opposite rotation. For example,q = quaternion(deg2rad([16 45 30]),'rotvec'); a = q*conj(q); rotatepoint(a,[0,1,0])ans = 0 1 0```

## Examples

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Create a quaternion scalar and get the complex conjugate.

`q = normalize(quaternion([0.9 0.3 0.3 0.25]))`
```q = quaternion 0.87727 + 0.29242i + 0.29242j + 0.24369k ```
`qConj = conj(q)`
```qConj = quaternion 0.87727 - 0.29242i - 0.29242j - 0.24369k ```

Verify that a quaternion multiplied by its conjugate returns a quaternion one.

`q*qConj`
```ans = quaternion 1 + 0i + 0j + 0k ```

## Input Arguments

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Quaternion to conjugate, specified as a scalar, vector, matrix, or array of quaternions.

Data Types: `quaternion`

## Output Arguments

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Quaternion conjugate, returned as a quaternion or array of quaternions the same size as `quat`.

Data Types: `quaternion`