Complex number has two parts; one is real part and second is imaginary part. Combined form of real part and imaginary part makes a Complex Number. Complex conjugate of a complex number is same as complex number. Difference in complex number and Complex Conjugate is that real parts are equal in both Numbers but imaginary part of complex conjugate has different sign than Imaginary Number of complex number. Let us see how to solve a complex numbers to complex conjugate.
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.