Sign In
The complex conjugate of a complex number has the same real part, but the imaginary part is the opposite of its original sign. Therefore, changing the sign of the imaginary part of a complex number creates its complex conjugate. It is denoted by a line drawn above the complex number.
a+bi = a-bi or a-bi = a+bi
For example, the complex conjugate of z = 3 - 5i is z= 3 + 5i. It is worth noting that the product of a complex number and its conjugate is a real number.
z= a+bi
a+bi= a-bi
Multiply
Add terms
i^2=- 1
- (- a)=a
This fact is very useful when simplifying quotients whose denominators are complex numbers.