Question

What’s the conjugate of $1+3i$?

Answer 1

Here in this question we have been asked to write the complex conjugate of the given complex number $1+3i$ for answering this question we will use definition of the complex conjugate complex number of any complex number $z=x+iy$ is given as $\bar{z}=x-iy$ that means we need to change the sign of the imaginary part.

Complete step-by-step answer:
Now considering from the question we have been asked to write the complex conjugate of the given complex number $1+3i$ .
From the basic concepts we know that a complex number has two parts, the real part and the imaginary part that contains the $i$ . The definition of the complex conjugate complex number of any complex number $z=x+iy$ is given as $\bar{z}=x-iy$ where $x$ is the real part and $y$ is the imaginary part of the complex number that means we need to change the sign of the imaginary part.
In the given complex number $1+3i=1+\left( 3 \right)i$ the real part is $1$ and imaginary part is $3$ so by changing the sign of the imaginary part we will be having $\overline{1+3i}=1-\left( 3 \right)i\Rightarrow 1-3i$ .
Therefore we can conclude that the complex conjugate of the given complex number $i$ will be given as $\Rightarrow 1-3i$.

Note: This is a very simple and easy question can be answered in a short span of time no confusions are possible in this generally. If observe the complex number $x+iy$ and its conjugate has the same magnitude that is the modulus or absolute value is same and given as $\sqrt{{{x}^{2}}+{{y}^{2}}}$ .