Question

How do you find the conjugate of $\left( 3-2i \right)$?

Answer 1

As we know that a complex number is represented as $a+ib$, where a and b are real numbers and $i$ is the imaginary part. Then we can find the conjugate of complex numbers by changing the sign of the imaginary part to its opposite sign.

Complete step by step solution:
We have been given a complex number $\left( 3-2i \right)$.
We have to find the conjugate of the given complex number.
We know that is expressed in the form of $a+ib$, where a and b are real numbers and $i$ is the imaginary part.
Now, the complex conjugate of the complex number of the form $a+ib$ is given as $a-ib$ and is represented by $\overline{z}$.
So we can find the complex conjugate of the number $\left( 3-2i \right)$ by changing the sign of the imaginary part by its opposite sign. Then we will get
$\Rightarrow 3+2i$
Hence we get the complex conjugate of $\left( 3-2i \right)$ as $3+2i$.

Note: The point to be remembered is that when we write the complex conjugate of the number the real part does not change. To find the conjugate the number must be written in the form $a+ib$, if not then then we have to convert the number into standard form. Then by simply changing the sign of the middle term we can find the conjugate. With the help of complex conjugate we can also find the roots of the polynomial.