Question

How do you find the complex conjugate of $5 - 4i$ ?

Answer 1

In this question, they have given a complex number $5 - 4i$ and asked us to find the complex conjugate of it. Conjugation is simply easy, we need to change the sign of the second term i.e. we need a change sign in the middle. Therefore we have changed positive sign to negative sign in the given complex number to find its conjugate. Finally we get the required answer.

Complete step by step answer:
Here, in this question, the given complex number is $5 - 4i$ and we need to change it to complex conjugate.
To conjugate any given equation or expression or complex number, we need to change its sign to its opposite sign. We have to change the sign in the middle of any equation or expression or complex number.
Here the given complex number is $5 - 4i$, in order to conjugate this we have to change the sign in the middle of the real number and an imaginary number i.e. change the negative sign to positive sign.

Therefore the complex conjugate of the given complex number $5 - 4i$ is $5 + 4i$.

Note: Students may get confused or may go wrong in understanding what conjugate or conjugation means.
In Algebra, the conjugation is a method where you should change the signs (+ to −, or − to +) between two terms.
Mostly conjugation is used to rationalise any equation, simply the complicated or congested equations to solve it more efficiently.
For example:
$3x{\text{ }} + {\text{ }}1\; \to 3x{\text{ }} - {\text{ }}1$ , where the sign in the middle of the given two terms is changed
Another example is $2z{\text{ }} - {\text{ }}7{\text{ }} \to {\text{ }}2z{\text{ }} + {\text{ }}7$ and $5i - 1 \to 5i + 1$ ,