Question

What’s the complex conjugate of $2i$ ?

Answer 1

Here in this question we have been asked to write the complex conjugate of the given complex number $2i$ 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 solution:
Now considering from the question we have been asked to write the complex conjugate of the given complex number $2i$ .
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 $2i=0+\left( 2 \right)i$ the real part is 0 and imaginary part is 2 so by changing the sign of the imaginary part we will be having $\overline{2i}=0-\left( 2 \right)i\Rightarrow -2i$ .
Therefore we can conclude that the complex conjugate of the given complex number $i$ will be given as $-2i$.

Note: This is a very simple and easy question that 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 $\sqrt{{{x}^{2}}+{{y}^{2}}}$ .