To determine the complex conjugate of a given complex number, you simply change the sign of the imaginary part while keeping the real part the same.
Given the complex number [tex]\( x = 3i \)[/tex]:
1. Identify the imaginary part: The imaginary part of [tex]\( 3i \)[/tex] is [tex]\( 3i \)[/tex].
2. Change the sign of the imaginary part: The opposite of [tex]\( +3i \)[/tex] is [tex]\( -3i \)[/tex].
Therefore, the complex conjugate of [tex]\( x = 3i \)[/tex] is [tex]\( -3i \)[/tex].
Among the given options, the correct answer is:
[tex]\[ x = -3i \][/tex]
