Question

Write the conjugate of 1/2+i

Answer 1

To find a conjugate of a binomial, simply change the signs between the two terms. For 1+2i, the conjugate is 1-2i.

Answer 2

Answer:

The conjugate of given number $\frac{1}{2+i}$ is  $\frac{2+i}{5}$

Step-by-step explanation:

Given : Number $\frac{1}{2+i}$

To find : Write the conjugate of the number?

Solution :

First we rationalize the given number

$\frac{1}{2+i}$

Multiply and divide by 2-i

$=\frac{1}{2+i}\times \frac{2-i}{2-i}$

$=\frac{2-i}{2^2-i^2}$

$=\frac{2-i}{4-(-1)}$

$=\frac{2-i}{4+1}$

$=\frac{2-i}{5}$

$=\frac{2}{5}-\frac{i}{5}$

The conjugate form of a complex number is changing the imaginary part sign.

The conjugate of $=\frac{2}{5}-\frac{i}{5}$ is $=\frac{2}{5}+\frac{i}{5}$

or $\frac{2+i}{5}$

Therefore, The conjugate of given number $\frac{1}{2+i}$ is  $\frac{2+i}{5}$