CONJUGATE OF A COMPLEX NUMBERS

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If two complex numbers which differ only in the sign of their imaginary parts are called conjugate complex numbers, that is, each complex number being conjugate of the other. It is denoted by clip_image002

Example

2 + 5i{\rm{ and }}2 - 5iare conjugates.

Ifz = a + bi, then its conjugate is\overline z  = a - bi

Conjugate of complex numbers is defined as follows:

z = a + bi \Rightarrow \overline z  = a - bi

Question 1:

Find the conjugate of z =  - 8 - 10i

Solution

z =  - 8 - 10i \Rightarrow \overline z  =  - 8 + 10i

Question 2:

Ifz =  - 4 + 6i, simplifyz + \overline z ?

Solution

We Know thati =  - 1,

z =  - 4 + 6i \Rightarrow \overline z  =  - 4 - 6i

Substitute the values as follows:

\begin{array}{c}
\left( { - 4 + 6i} \right) + \left( { - 4 - 6i} \right) =  - 4 - 4 + 6i - 6i\\
 =  - 8
\end{array}

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