Magnitude of complex number and complex conjugate are equal as they have same real and imaginary parts. If there is a complex number like 2 + 3i then complex conjugate of this number will be 2 – 3i. Here 'i' stands for imaginary number. We denote complex conjugate by '*' sign. If complex number is 'z' then complex conjugate will be z*.
There are some properties which are used to solve a complex number to a complex conjugate:
Property 1: Complex number 'z' and complex conjugate z* will be equal if and only if 'z' is real.
Property 2: Magnitude of complex number |z| and complex conjugate |z*| is always equal.
Property 3: Square of magnitude of complex number is equals to multiplication of complex number and complex conjugate. We can write it as:
|z|2 = zz* = z*z.
This will give same result.
Property 4: If we find complex conjugate z* of complex number 'z' then other complex conjugate of z* will give complex number 'z' again. We can write it as z** = z.
Property 5: Inverse of complex number can be calculated by division of z* and |z|2.