The modulus of a complex number gives the distance of the complex number from the origin in the Argand plane, whereas the conjugate of a complex number gives the reflection of the complex number about the real axis in the Argand plane.
Conjugate of a Complex Number
Fig 1 - Conjugate of a complex number
The representation of a complex number and its conjugate in the Argand plane are, respectively , the points and
Geometrically , the point is the mirror image of the point on the real axis (Fig 1)
Example
Find the conjugate of
Answer: The conjugate of
Modulus of a Complex Number
Fig 2 - Modulus of a complex number
In the Argand plane, the modulus of the complex number is
is the distance between the point representing the complex number and representing the origin (Fig 2).
Example
Find the modulus of the complex number